Graft copolymers of polyfarnesenes with condensation polymers

ABSTRACT

Provided herein are graft copolymers of polyfarnesenes with condensation polymers; and methods of making and using the graft copolymers disclosed herein. In certain embodiments, the condensation polymers include polyesters, polycarbonates, polyamides, polyethers, phenol-formaldehyde resins, urea-formaldehyde resins, melamine-formaldehyde resins and combinations thereof. In some embodiments, the polyfarnesenes include farnesene homopolymers derived from a farnesene, and farnesene interpolymers derived from a farnesene and at least a vinyl monomer. In certain embodiments, the farnesene is prepared from a sugar by using a microorganism.

PRIOR RELATED APPLICATION

This is a U.S. national stage application of the International Patent Application No. PCT/US2011/045856, filed Jul. 29, 2011, which claims the benefit of U.S. Provisional Patent Application No. 61/369,758, filed Aug. 2, 2010, which is incorporated herein by reference in their entirety.

FIELD OF THE INVENTION

This invention provides graft copolymers of polyfarnesenes with condensation polymers; and the processes of making and using the graft copolymers disclosed herein. In certain embodiments, the condensation polymers are polyesters, polycarbonates, polyamides, polyethers, phenol-formaldehyde resins, urea-formaldehyde resins, melamine-formaldehyde resins and combinations thereof. In some embodiments, the polyfarnesenes are farnesene homopolymers derived from a farnesene, or farnesene interpolymers derived from a farnesene and at least a vinyl monomer.

BACKGROUND OF THE INVENTION

A polyolefin is a polymer prepared generally by polymerizing an olefin such as alkenes having the general formula C_(n)H_(2n). In general, the physical, chemical or biological properties of polyolefins may be modified by copolymerizing olefins or polyolefins with a variety of other monomers or polymers to form olefin copolymers. The olefin copolymers can be prepared in various types such as random copolymers, alternating copolymers, block copolymers or graft copolymers. The olefin graft copolymers can be prepared by reacting modified polyolefins with other polymers such as polyesters or polycarbonates.

Generally, polyolefins are derived from olefins manufactured by cracking petroleum or coal tar. In the cracking process, large alkanes are broken apart at high temperatures in the presence of a catalyst to yield smaller olefins. In general, the cracking process is not environmental friendly. Moreover, the olefins from the cracking process are generally derived from a non-renewable source.

Therefore, there is a need for more environmentally friendly and/or renewable polymers, for instance, polymers derived from isoprenoid compounds that can be obtained from natural sources. Further, there is also a need for novel polymers that have unique physical, chemical and biological properties.

SUMMARY OF THE INVENTION

The aforementioned needs can be met by various aspects of the invention disclosed herein. In one aspect, provided herein is a graft copolymer of a polyfarnesene with a condensation polymer.

In certain embodiments, the polyfarnesene has formula (A):

wherein n is an integer from 1 to about 100,000; m is an integer from 0 to about 100,000; X is derived from a farnesene; and Y is derived from a vinyl monomer. In some embodiments, when m is 0, n is from about 2 to about 100,000. In other embodiments, when m is 1 or greater, the mole percent ratio of X to Y is from about 1:4 to about 100:1.

In some embodiments, X of formula (A) has one or more of formulae (I)-(VIII) and stereoisomers thereof:

-   wherein R¹ has formula (XI):

-   R² has formula (XII):

-   R³ has formula (XIII):

-    and -   R⁴ has formula (XIV):

In certain embodiments, Y of formula (A) has formula (IX) or a stereoisomer thereof:

-   wherein each of R⁵, R⁶, R⁷ and R⁸ is independently H, alkyl,     cycloalkyl, aryl, alkenyl, cycloalkenyl, alkynyl, heterocyclyl,     alkoxy, aryloxy, carboxy, alkoxycarbonyl, aminocarbonyl,     alkylaminocarbonyl, dialkylamino carbonyl, acyloxy, nitrile or halo.

In another aspect, provide herein is a modified polyfarnesene prepared by reacting a polyfarnesene with at least one modifier in the presence of a grafting initiator, radiation or a combination thereof, wherein the ratio of the polyfarnesene to the modifier is from about 100,000:1 to about 100:5 by weight.

In some embodiments, the modifier has formula (XVI), (XVII), (XVIII), (XIX), or (XX):

wherein each of Q¹ and Q⁶ is independently O, S, NR²³ or N-Q⁷; each of Q², Q³, Q⁴ and Q⁵ is independently halo, Q⁸, NR²⁴R²⁵, OR²⁶ or O-Q⁸; Q⁷ and Q⁸ respectively have the following formulae:

wherein k is an integer from 1 to about 10; and Q⁹ is OH, NH₂, NHR³⁰, carboxyl, epoxy or gycidyl; and

each of R⁹ to R³⁰ is independently H, C₁₋₂₀ alkyl, C₁₋₂₀ alkenyl, C₁₋₂₀ alkynyl, cycloalkyl, aryl, aralkyl, alkaryl, OH, NH₂, carboxyl, epoxy or gycidyl, or R¹⁹ and R²² together form a —(CH₂)_(m)— group where m is an integer from 1 to about 6, and wherein each of the C₁₋₂₀ alkyl, C₁₋₂₀ alkenyl, C₁₋₂₀ alkynyl, cycloalkyl, aryl, aralkyl, alkaryl, epoxy, gycidyl and —(CH₂)_(m)— is optionally substituted.

In another aspect, provide herein is a graft copolymer prepared by reacting a modified polyfarnesene disclosed herein with a condensation polymer disclosed herein at a temperature from about 50° C. to about 300° C. In some embodiments, the condensation polymer is a polyester, polycarbonate, polyamide, polyether, phenol-formaldehyde resin, urea-formaldehyde resin, melamine-formaldehyde resin or a combination thereof. In certain embodiments, the condensation polymer is a polyester, polycarbonate, polyamide or a combination thereof. In some embodiments, the condensation polymer is a polyester. In other embodiments, the polyester is a polyethylene terephthalate (PET).

In another aspect, provide herein is a polymer composition comprising the graft copolymer disclosed herein and at least an additive. In some embodiments, the additive is a filler, tackifier, slip agent, anti-blocking agent, plasticizer, antioxidant, blowing agent, blowing agent activator, UV stabilizer, acid scavenger, colorant or pigment, coagent, lubricant, antifogging agent, flow aid, processing aid, extrusion aid, coupling agent, cross-linking agent, stability control agent, nucleating agent, surfactant, flame retardant, antistatic agent or a combination thereof.

In another aspect, provide herein is an article comprising the graft copolymer disclosed herein. In some embodiments, the article is a molded article, film, sheet or foam. In other embodiments, the article is a molded article selected from toys, grips, soft touch handles, bumper rub strips, floorings, auto floor mats, wheels, casters, furniture and appliance feet, tags, seals, gaskets such as static and dynamic gaskets, automotive doors, bumper fascia, grill components, rocker panels, hoses, linings, office supplies, seals, liners, diaphragms, tubes, lids, stoppers, plunger tips, delivery systems, kitchen wares, shoes, shoe bladders, and shoe soles.

Additional aspects of the invention and characteristics and properties of various embodiments of the invention become apparent with the following description.

DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts Ultraviolet-Visible (UV-Vis) spectra of Example 1 and β-farnesene.

FIG. 2 depicts a Gel Permeation Chromatography (GPC) curve of Example 1.

FIG. 3 depicts a C¹³ Nuclear Magnetic Resonance (NMR) spectrum of Example 1.

FIG. 4 depicts a H¹ NMR spectrum of Example 1.

FIG. 5 depicts a Differential Scanning calorimetry (DSC) curve of Example 1.

FIG. 6 depicts a Thermal Gravimetric Analysis (TGA) curve of Example 1 measured in air.

FIG. 7 depicts a TGA curve of Example 1 measured in nitrogen.

FIG. 8 depicts lap test results of Example 1.

FIG. 9 depicts a GPC curve of Example 2.

FIG. 10 depicts a DSC curve of Example 2.

FIG. 11 depicts tensile test results of Example 2.

FIG. 12 depicts a GPC curve of Example 3.

FIG. 13 depicts a C¹³ NMR spectrum of Example 3.

FIG. 14 depicts a H¹ NMR spectrum of Example 3.

FIG. 15 depicts a DSC curve of Example 3.

FIG. 16 depicts a TGA curve of Example 3.

FIG. 17 depicts lap test results of Example 3.

FIG. 18 depicts a GPC curve of polystyrene formed.

FIG. 19 depicts a GPC curve of polystyrene-1,4-polyfarnesene di-block copolymer formed.

FIG. 20 depicts a GPC curve of Example 4.

FIG. 21 depicts a ¹³C NMR spectrum of Example 4.

FIG. 22 depicts a ¹H NMR spectrum of Example 4.

FIG. 23 depicts a DSC curve of Example 4.

FIG. 24 depicts a TGA curve of Example 4.

FIG. 25 depicts tensile test results of Example 4.

FIG. 26 depicts lap test results of Example 4.

FIG. 27 depicts a GPC curve of polystyrene formed.

FIG. 28 depicts a GPC curve of polystyrene-3,4-polyfarnesene di-block copolymer formed.

FIG. 29 depicts a GPC curve of Example 5.

FIG. 30 depicts a ¹³C NMR spectrum of Example 5.

FIG. 31 depicts a ¹H NMR spectrum of Example 5.

FIG. 32 depicts a DSC curve of Example 5.

FIG. 33 depicts a TGA curve of Example 5.

FIG. 34 depicts tensile test results of Example 5.

FIG. 35 depicts a GPC curve of Example 5 after extraction with hexane.

FIG. 36 depicts a GPC curve of hexane after extraction for Example 5.

FIG. 37 depicts tensile test results of Example 5.

DETAILED DESCRIPTION OF THE INVENTION

General Definitions

“Polymer” refers to a polymeric compound prepared by polymerizing monomers, whether of the same or a different type. The generic term “polymer” embraces the terms “homopolymer,” “copolymer,” “terpolymer” as well as “interpolymer.”

“Interpolymer” refers to a polymer prepared by the polymerization of at least two different types of monomers. The generic term “interpolymer” includes the term “copolymer” (which generally refers to a polymer prepared from two different monomers) as well as the term “terpolymer” (which generally refers to a polymer prepared from three different types of monomers). It also encompasses polymers made by polymerizing four or more types of monomers.

“Graft copolymer” refers to a copolymer comprising a first polymer X branching from the backbone of a second polymer Y. Each of the first polymer X and the second polymer Y can be independently a homopolymer or an interpolymer. A graft copolymer of X with Y can be represented by the formula X-g-Y. For example, polyfarnesene-g-polyester represents a graft copolymer of a polyfarnesene with a polyester. Similarly, polyfarnesene-g-PET represents a graft copolymer of a polyfarnesene with a PET.

“Condensation polymer” refers to a polymer formed by condensation polymerization in which small molecules, such as water or methanol, are released as by-products, as opposed to an addition polymer which involves the reaction of unsaturated monomers. Some non-limiting examples of condensation polymers include polyesters, polycarbonates, polyamides, polyethers, phenol-formaldehyde resins, urea-formaldehyde resins, melamine-formaldehyde resins and polyacetals. Some non-limiting examples of the condensation polymers are described in Malcolm Stevens, “Polymer Chemistry: An Introduction,” Oxford University Press, New York, pp. 285-408 (1999), which is incorporated herein by reference.

“Organyl” refers to any organic substituent group, regardless of functional type, having one free valence at a carbon atom, e.g., CH₃CH₂—, ClCH₂—, CH₃C(═O)—, 4-pyridylmethyl.

“Hydrocarbyl” refers to any univalent group formed by removing a hydrogen atom from a hydrocarbon, such as alkyl (e.g., ethyl), cycloalkyl (e.g., cyclohexyl) and aryl (e.g., phenyl).

“Heterocyclyl” refers to any univalent group formed by removing a hydrogen atom from any ring atom of a heterocyclic compound.

“Alkyl” or “alkyl group” refers to a univalent group having the general formula C_(n)H_(2n+1) derived from removing a hydrogen atom from a saturated, unbranched or branched aliphatic hydrocarbon, where n is an integer, or an integer between 1 and 20, or between 1 and 8. Examples of alkyl groups include, but are not limited to, (C₁-C₈)alkyl groups, such as methyl, ethyl, propyl, isopropyl, 2-methyl-1-propyl, 2-methyl-2-propyl, 2-methyl-1-butyl, 3-methyl-1-butyl, 2-methyl-3-butyl, 2,2-dimethyl-1-propyl, 2-methyl-1-pentyl, 3-methyl-1-pentyl, 4-methyl-1-pentyl, 2-methyl-2-pentyl, 3-methyl-2-pentyl, 4-methyl-2-pentyl, 2,2-dimethyl-1-butyl, 3,3-dimethyl-1-butyl, 2-ethyl-1-butyl, butyl, isobutyl, t-butyl, pentyl, isopentyl, neopentyl, hexyl, heptyl and octyl. Longer alkyl groups include nonyl and decyl groups. An alkyl group can be unsubstituted or substituted with one or more suitable substituents. Furthermore, the alkyl group can be branched or unbranched. In some embodiments, the alkyl group contains at least 2, 3, 4, 5, 6, 7, or 8 carbon atoms.

“Cycloalkyl” or “cycloalkyl group” refers to a univalent group derived from a cycloalkane by removal of a hydrogen atom from a non-aromatic, monocyclic or polycyclic ring comprising carbon and hydrogen atoms. Examples of cycloalkyl groups include, but are not limited to, (C₃-C₇)cycloalkyl groups, such as cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, and cycloheptyl, and saturated cyclic and bicyclic terpenes and (C₃-C₇)cycloalkenyl groups, such as cyclopropenyl, cyclobutenyl, cyclopentenyl, cyclohexenyl, and cycloheptenyl, and unsaturated cyclic and bicyclic terpenes. A cycloalkyl group can be unsubstituted or substituted by one or two suitable substituents. Furthermore, the cycloalkyl group can be monocyclic or polycyclic. In some embodiments, the cycloalkyl group contains at least 5, 6, 7, 8, 9, or 10 carbon atoms.

“Aryl” or “aryl group” refers to an organic radical derived from a monocyclic or polycyclic aromatic hydrocarbon by removing a hydrogen atom. Non-limiting examples of the aryl group include phenyl, naphthyl, benzyl, or tolanyl group, sexiphenylene, phenanthrenyl, anthracenyl, coronenyl, and tolanylphenyl. An aryl group can be unsubstituted or substituted with one or more suitable substituents. Furthermore, the aryl group can be monocyclic or polycyclic. In some embodiments, the aryl group contains at least 6, 7, 8, 9, or 10 carbon atoms.

“Isoprenoid” and “isoprenoid compound” are used interchangeably herein and refer to a compound derivable from isopentenyl diphosphate.

“Substituted” as used to describe a compound or chemical moiety refers to that at least one hydrogen atom of that compound or chemical moiety is replaced with a second chemical moiety. The second chemical moiety can be any desired substituent that does not adversely affect the desired activity of the compound. Examples of substituents are those found in the exemplary compounds and embodiments disclosed herein, as well as halogen; alkyl; heteroalkyl; alkenyl; alkynyl; aryl, heteroaryl, hydroxyl; alkoxyl; amino; nitro; thiol; thioether; imine; cyano; amido; phosphonato; phosphine; carboxyl; thiocarbonyl; sulfonyl; sulfonamide; carbonyl; formyl; carbonyloxy; oxo; haloalkyl (e.g., trifluoromethyl); carbocyclic cycloalkyl, which can be monocyclic or fused or non-fused polycyclic (e.g., cyclopropyl, cyclobutyl, cyclopentyl or cyclohexyl) or a heterocycloalkyl, which can be monocyclic or fused or non-fused polycyclic (e.g., pyrrolidinyl, piperidinyl, piperazinyl, morpholinyl or thiazinyl); carbocyclic or heterocyclic, monocyclic or fused or non-fused polycyclic aryl (e.g., phenyl, naphthyl, pyrrolyl, indolyl, furanyl, thiophenyl, imidazolyl, oxazolyl, isoxazolyl, thiazolyl, triazolyl, tetrazolyl, pyrazolyl, pyridinyl, quinolinyl, isoquinolinyl, acridinyl, pyrazinyl, pyridazinyl, pyrimidinyl, benzimidazolyl, benzothiophenyl or benzofuranyl); amino (primary, secondary or tertiary); o-lower alkyl; o-aryl, aryl; aryl-lower alkyl; —CO₂CH₃; —CONH₂; —OCH₂CONH₂; —NH₂; —SO₂NH₂; —OCHF₂; —CF₃; —OCF₃; —NH(alkyl); —N(alkyl)₂; —NH(aryl); —N(alkyl)(aryl); —N(aryl)₂; —CHO; —CO(alkyl); —CO(aryl); —CO₂(alkyl); and —CO₂(aryl); and such moieties can also be optionally substituted by a fused-ring structure or bridge, for example —OCH₂O—. These substituents can optionally be further substituted with a substituent selected from such groups. All chemical groups disclosed herein can be substituted, unless it is specified otherwise.

“Organolithium reagent” refers to an organometallic compound with a direct bond between a carbon and a lithium atom. Some non-limiting examples of organolithium reagents include vinyllithium, aryllithium (e.g., phenyllithium), and alkyllithium (e.g., n-butyl lithium, sec-butyl lithium, tent-butyl lithium, methyllithium, isopropyllithium or other alkyllithium reagents having 1 to 20 carbon atoms).

A composition that is “substantially free” of a compound means that the composition contains less than about 20 wt. %, less than about 10 wt. %, less than about 5 wt. %, less than about 3 wt. %, less than about 1 wt. %, less than about 0.5 wt. %, less than about 0.1 wt. %, or less than about 0.01 wt. % of the compound, based on the total volume of the composition.

A polymer that is “substantially linear” means that the polymer contains less than about 20 wt. %, less than about 10 wt. %, less than about 5 wt. %, less than about 3 wt. %, less than about 1 wt. %, less than about 0.5 wt. %, less than about 0.1 wt. %, or less than about 0.01 wt. % of the branched, star-shaped or other regular or irregular structures, based on the total volume of the composition.

A polymer that is “substantially branched” means that the polymer contains less than about 20 wt. %, less than about 10 wt. %, less than about 5 wt. %, less than about 3 wt. %, less than about 1 wt. %, less than about 0.5 wt. %, less than about 0.1 wt. %, or less than about 0.01 wt. % of the linear, star-shaped or other regular or irregular structures, based on the total volume of the composition.

A polymer that is “substantially star-shaped” means that the polymer contains less than about 20 wt. %, less than about 10 wt. %, less than about 5 wt. %, less than about 3 wt. %, less than about 1 wt. %, less than about 0.5 wt. %, less than about 0.1 wt. %, or less than about 0.01 wt. % of the branched, linear or other regular or irregular structures, based on the total volume of the composition.

In the following description, all numbers disclosed herein are approximate values, regardless whether the word “about” or “approximate” is used in connection therewith. They may vary by 1 percent, 2 percent, 5 percent, or, sometimes, 10 to 20 percent. Whenever a numerical range with a lower limit, R^(L), and an upper limit, R^(U), is disclosed, any number falling within the range is specifically disclosed. In particular, the following numbers within the range are specifically disclosed: R=R^(L)+k*(R^(U)—R^(L)), wherein k is a variable ranging from 1 percent to 100 percent with a 1 percent increment, i.e., k is 1 percent, 2 percent, 3 percent, 4 percent, 5 percent, . . . , 50 percent, 51 percent, 52 percent, . . . , 95 percent, 96 percent, 97 percent, 98 percent, 99 percent, or 100 percent. Moreover, any numerical range defined by two R numbers as defined in the above is also specifically disclosed.

The graft copolymers disclosed herein generally comprise a polyfarnesene grafted with a condensation polymer. In some embodiments, the condensation polymer is a polyester, polycarbonate, polyamide, polyether, phenol-formaldehyde resin, urea-formaldehyde resin, melamine-formaldehyde resin or a combination thereof. In certain embodiments, the condensation polymer is a polyester, polycarbonate, polyamide or a combination thereof. In certain embodiments, the condensation polymer is a polyester. In other embodiments, the polyester is a polyethylene terephthalate (PET). In some embodiments, the condensation polymer disclosed herein is substantially free of one or more of a polyester, polycarbonate, polyamide, polyether, phenol-formaldehyde resin, urea-formaldehyde resin and melamine-formaldehyde resin.

In some embodiments, the condensation polymer disclosed herein is a polyester. Any polyester having repeating ester groups in its backbone and reactive end groups can be used herein. In some embodiments, the reactive end groups are hydroxyl, carboxyl, epoxy or a combination thereof. In other embodiments, the reactive end groups are free of hydroxyl, carboxyl, or epoxy. In certain embodiments, the polyester is a hydroxyl-terminated polyester, a carboxyl-terminated polyester, or an epoxy-terminated polyester.

The polyester disclosed herein can be obtained by any method known in the literature. In some embodiments, the polyester is prepared by direct esterification of a diol with a diacid. In other embodiments, the polyester is prepared by transesterification of a diol with a diester. In certain embodiments, the polyester is prepared by reacting a diol with a diacyl halide. In some embodiments, the polyester is prepared by reacting a diol with a dianhydride. In certain embodiments, the polyester is prepared by ring-opening polymerization of a lactone or a cyclic ester such as α-acetolactone, β-propiolactone, γ-butyrolactone, δ-valerolactone, caprolactone, and the like. In some embodiments, the polyester is prepared by intermolecular self-condensation reaction of one or more hydroxy acids, such as 2-hydroxypropanoic acid (i.e., lactic acid), glycolic acid, citric acid, mandelic acid, 3-hydroxypropanoic acid, 2-hydroxybutyric acid, 3-hydroxybutyric acid, 4-hydroxybutyric acid and 3-hydroxyvaleric acid.

The polyester disclosed herein can be any polyester or copolyester having 2 or more reactive end groups selected from hydroxy, carboxyl, epoxy and combinations thereof. Some non-limiting examples of the polyester include polyglycolic acid (PGA), polylactic acid (PLA), polycaprolactone (PCL), polyethylene adipate (PEA), polyhydroxyalkanoates (PHAs), polyethylene terephtalate (PET), polybutylene terephthalate (PBT), polytrimethylene terephthalate (PTT), polyethylene naphthalate (PEN), polyhexamethylene terephthalate (PHT), polycyclohexane-1,4-dimethylolterephthalate (PCT), polyneopentyl terephthalate (PNT). In some embodiments, the polyester disclosed herein is a polyethylene terephtalate (PET). In certain embodiments, the PET contains two reactive end groups selected from hydroxy, carboxyl, epoxy and combinations thereof.

Some non-limiting examples of the copolyester include (a) copolyesters derived from ethylene glycol and terephthalic acid and isophthalic acid and/or phthalic acid; and (b) copolyesters derived from ethylene glycol, 1,4-cyclohexane dimethanol and dimethyl terephthalate or terephthalic acid (e.g., PCTG, PETG or PET-CHDM). The PCTG, PETG and PET-CHDM polymers can be derived from ethylene glycol, 1,4-cyclohexane dimethanol and dimethyl terephthalate or terephthalic acid. Their generic structure can be represented by formula (B) as shown below.

wherein the asterisks (*) are end groups (e.g., OH or H); y is from 0.5 to 0.99; and x is from 0.5 to 0.01. PCTG, PETG and PCT can be distinguished from each other by the values of x and y. For example, y is from 0.05 to 0.5 and x is from 0.95 to 0.5 for PETG; y is 1.0 and x is 0 for PCT; and y is from 0.01 to 0.05 and x is from 0.99 to 0.95 for PET-CHDM.

In some embodiments, y of the formula (B) is from 0.5 to 0.99 and x is from 0.5 to 0.01. In other embodiments, y of formula (B) is from 0.55 to 0.95 and x is from 0.45 to 0.05. In further embodiments, y of formula (B) is from 0.6 to 0.9 and x is from 0.4 to 0.1. In still further embodiments, y of formula (B) is from 0.65 to 0.85 and x is from 0.35 to 0.15.

In certain embodiments, the polyester is derived from a monomer prepared from a biological source (such as sugars and lipids) by a biological process such as bacterial fermentation. Some non-limiting examples of biologically prepared monomers include lactic acid, glycolic acid and citric acid. In some embodiments, the polyester itself is prepared from a biological source (such as sugars and lipids) by a biological process such as bacterial fermentation. Some non-limiting examples of biologically prepared polyesters include polyhydroxyalkanoates such as poly-(R)-3-hydroxybutyrate (P3HB), poly-3-hydroxyvalerate (PHV), poly-4-hydroxybutyrate (P4HB), and poly(3-hydroxybutyrate-co-3-hydroxyvalerate (PHBV). In some embodiments, the polyester disclosed herein is biodegradable. In certain embodiments, the polyester disclosed herein is biocompatibility. In some embodiments, the polyester disclosed herein is a bioplastic.

The end groups of formula (B) or the polyester disclosed herein can be varied according to the properties desired. In some embodiments, the end groups are H, OH or a mixture thereof. In other embodiments, the OH end group can be modified by reacting with a carboxylic acid to form an ester end group or with an epoxy halide compound, such as epichlorohydrin, to form an epoxy end group.

In some embodiments, the polyester disclosed herein is or comprises PGA, PLA, PCL, PEA, PHA, PET, PBT, PTT, PEN, PHT, PCT, PNT, PCTG, PETG, PET-CHDM, P3HB, PHV, P4HB, PHBV or a combination thereof. In some embodiments, the polyester disclosed herein is substantially free of one or more of PGA, PLA, PCL, PEA, PHA, PET, PBT, PTT, PEN, PHT, PCT, PNT, PCTG, PETG, PET-CHDM, P3HB, PHV, P4HB and PHBV.

In some embodiments, the condensation polymer disclosed herein is a polycarbonate. Any polycarbonate having repeating carbonate groups in its backbone and reactive end groups can be used herein. In certain embodiments, the reactive end groups are hydroxy, which optionally can be converted into other reactive end groups by methods disclosed herein. In some embodiments, the polycarbonate is a hydroxyl-terminated polycarbonate or an epoxy-terminated polycarbonate.

The polycarbonate disclosed herein can be obtained by any method known in the literature. In some embodiments, the polycarbonate is prepared by reacting a diol with a carbonate precursor such as phosgene, a halo-formate or carbonate ester. In certain embodiments, the polycarbonate is prepared by transesterification of a diol with a carbonate ester such as diphenyl carbonate. Some non-limiting examples of suitable diols include bisphenols, aliphatic diols such as glycols and combinations thereof. Some non-limiting examples of suitable bisphenols include bisphenyl A, bisphenyl AP, bisphenyl AF, bisphenyl B, bisphenyl BP, bisphenyl C, bisphenyl E, bisphenyl F, bisphenyl G, bisphenyl M, bisphenyl S, bisphenyl P, bisphenyl PH, bisphenyl TMC, bisphenyl Z and combinations thereof. In some embodiments, the polycarbonate is derived from bisphenyl A and a carbonate precursor such as phosgene.

In certain embodiments, the condensation polymer disclosed herein is a polyamide. Any polyamide having repeating amide groups in its backbone and reactive end groups can be used herein. In some embodiments, the reactive end groups are amino, carboxyl or a combination thereof. The reactive end groups optionally can be converted into other reactive end groups by methods disclosed herein. In certain embodiments, the polyamide is an amino-terminated polyamide, a carboxyl-terminated polyamide or an epoxy-terminated polyamide.

The polyamide disclosed herein can be obtained by any method known in the literature. In some embodiments, the polyamide is prepared by reacting a diamine with a diacid. In other embodiments, the polyamide is prepared by reacting a diamine with a diester. In certain embodiments, the polyamide is prepared by reacting a diamine with a diacyl halide. In some embodiments, the polyamide is prepared by reacting a diamine with a dianhydride. In certain embodiments, the polyamide is prepared by ring-opening polymerization of a lactam or a cyclic amide such as caprolactam, α-lactam, β-lactam, γ-lactam, δ-lactam, and the like.

In some embodiments, the polyamide is prepared by intermolecular self-condensation reaction of one or more amino acids. Any amino acid containing an amine group and a carboxylic acid group can be used herein. In some embodiments, the amino acid has the formula H₂N(CHR)_(n)COOH where n is an integer from about 1 to about 20; and R is H, alkyl, cycloalkyl, alkenyl, aryl, alkaryl, aryalkyl, heterocyclyl or heteroaryl wherein the alkyl, cycloalkyl, alkenyl, aryl, alkaryl, aryalkyl, heterocyclyl or heteroaryl is optionally substituted. Some non-limiting examples of suitable amino acids include isoleucine, alanine, leucine, asparagine, lysine, aspartic acid, methionine, cysteine, phenylalanine, glutamic acid, threonine, glutamine, tryptophan, glycine, valine, proline, selenocysteine, serine, tyrosine, arginine, histidine, ornithine, taurine and combinations thereof. In some embodiments, the polyamide disclosed herein is biodegradable. In certain embodiments, the polyamide disclosed herein is biocompatibility. In some embodiments, the polyamide disclosed herein is a bioplastic.

In some embodiments, the condensation polymer disclosed herein is a polyether. Any polyether having repeating ether groups in its backbone and reactive end groups can be used herein. In some embodiments, the reactive end groups are hydroxy, which optionally can be converted into other reactive end groups by methods disclosed herein. In certain embodiments, the polyether is a hydroxyl-terminated polyether or an epoxy-terminated polyether. In certain embodiments, the polyether is a hydroxyl-terminated polyether or an epoxy-terminated polyether.

The polyether disclosed herein can be obtained by any method known in the literature. In some embodiments, the polyether is prepared by intermolecular self-condensation reaction of one or more diols such as aliphatic glycols (e.g., 1,3-propanediol) and benzylic glycols. In some embodiments, the polyether is prepared by reacting a diol (e.g., bisphenols) with a dihalo compound (e.g., dihaloaromatic compounds and dihaloalkanes such as dichloromethane) under a basic condition.

In some embodiments, the condensation polymer disclosed herein is a phenol-aldehyde resin such as phenol-formaldehyde resin. Some non-limiting examples of phenol-aldehyde resins are described in Gardziella, L. A. Pilato, and A. Knop, “Phenolic Resins: Chemistry, Applications, Standardization, Safety and Ecology,” 2^(nd) Edition, Springer-Verlag, New York, Chapter 2, pp. 24-79 (1999), which is incorporated herein by reference.

Any phenol-aldehyde resin that can be prepared from a phenol compound and an aldehyde under either an acid condition or a basic condition can be used herein. In some embodiments, the phenol compound has formula (C):

wherein each of R_(a), R_(b), R_(c), R_(d) and R_(e) of the phenol compound of formula (C) is independently hydrogen; hydroxy; halide such as fluoride, chloride, bromide and iodide; nitro; benzo; carboxy; alkoxycarbonyl; acyl such as formyl, alkylcarbonyl (e.g. acetyl) and arylcarbonyl (e.g., benzoyl); alkyl such as methyl, ethyl, propyl, butyl, pentyl, hexyl, heptyl, octyl, nonyl, decyl, and the like; aryl such as phenyl and naphthyl; aralkyl such as benzyl; or alkaryl such as alkylphenyls. In certain embodiments, each of R_(a), R_(b), R_(d) and R_(e) of the phenol compound of formula (C) is independently H; and R_(c) is alkyl. In other embodiment, each of R_(a), R_(b), R_(c), R_(d) and R_(e) of the phenol compound of formula (C) is H.

In certain embodiments, the phenol compound has formula (D):

wherein each of R_(f), R_(g), R_(h) and R_(i) is independently hydrogen; hydroxy; halide such as fluoride, chloride, bromide and iodide; nitro; benzo; carboxy; acyl such as formyl, alkylcarbonyl (e.g. acetyl) and arylcarbonyl (e.g., benzoyl); alkyl such as methyl, ethyl, propyl, butyl, pentyl, hexyl, heptyl, octyl, nonyl, decyl, and the like; alkenyl such as unsubstituted or substituted vinyl and allyl; unsubstituted or substituted methacrylate; unsubstituted or substituted acrylate; silyl ether; siloxanyl; aryl such as phenyl and naphthyl; aralkyl such as benzyl; or alkaryl such as alkylphenyls. In some embodiment, each of R_(f), R_(g), R_(h) and R_(i) of the phenol compound of formula (D) is H. In other embodiment, each of R_(f), R_(h) and R_(i) of the phenol compound of formula (D) is H; and R_(g) is alkyl.

Any aldehyde that reacts with the phenol compounds disclosed herein can be used to prepare the phenol-aldehyde resin disclosed herein. In some embodiments, the aldehyde is represented by formula (E): R_(j)—CH═O  (E) wherein R_(j) is H, alkyl, substituted alkyl such as aralkyl, aryl, or substituted aryl such as alkaryl. In certain embodiments, R_(j) is alkyl. In other embodiments, R_(j) is C₁₋₂₂ alkyl such as methyl, ethyl, propyl, isopropyl, butyl, isobutyl, pentyl, isopentyl, hexyl, octyl, nonyl, decyl, dodecyl, tetradecyl, hexadecyl, octadecyl, benzyl and the like. In some embodiments, R_(j) is a C₃₋₂₂ alkyl group. In certain embodiments, R_(j) is a C₃ alkyl group. In other embodiments, R_(j) is H, i.e., the aldehyde is formaldehyde. The term “formaldehyde” also encompasses any substance that can split off or release formaldehyde, such as paraformaldehyde and trioxane.

Generally, the phenol-aldehyde resin disclosed herein can be prepared by two different methods. The first method utilizes a stoichiometric excess of the phenolic compound (e.g., phenol or resorcinol) over the aldehyde (e.g., formaldehyde) in the presence of an acidic catalyst to form a phenolic novolac or novolak. The novolak generally requires the addition of a methylene donor such as formaldehyde, paraformaldehyde or hexamethylenetetramine (HEXA) to effect curing. The other method utilizes a stoichiometric excess of the aldehyde (e.g., formaldehyde) over the phenolic compound (e.g., phenol or resorcinol) in the presence of a base catalyst to form a phenolic resole. The phenolic resole can be subsequently cured to a thermosetting polymer simply by heating or the addition of an acid catalyst.

In some embodiments, the aldehyde is an alkyl aldehyde such as n-butyraldehyde, isobutyraldehyde, valeraldehyde, lauryl aldehyde, palmityl aldehyde, stearyl aldehyde or a combination thereof. In further embodiments, the aldehyde is formaldehyde, an alkyl aldehyde or a combination thereof. When a mixture of aldehydes are used, they can be added to the reaction mixture individually, simultaneously or sequentially.

In some embodiments, the reactive end groups of the phenol-aldehyde resin disclosed herein are hydroxy, which optionally can be converted into other reactive end groups by methods disclosed herein.

In some embodiments, the condensation polymer disclosed herein is a urea-formaldehyde resin. Any urea-formaldehyde resin prepared by reacting urea with formaldehyde and having methylol end groups can be used herein. In some embodiments, the methylol end groups optionally can be converted into other reactive end groups. In certain embodiments, the formaldehyde is replaced partially or totally with one or more aldehydes disclosed herein. In some embodiments, the urea is a substituted urea. In certain embodiments, the urea is replaced partially or totally with one or more phenol compounds disclosed herein. Some non-limiting examples of urea-formaldehyde resins are described in Beat Meyer, “Urea-Formaldehyde Resins,” Addison-Wesley Pub. (1979), which is incorporated herein by reference.

In some embodiments, the condensation polymer disclosed herein is a melamine-formaldehyde resin. Any melamine-formaldehyde resin prepared by reacting melamine with formaldehyde and having methylol end groups can be used herein. In some embodiments, the methylol end groups optionally can be converted into other reactive end groups. In certain embodiments, the formaldehyde is replaced partially or totally with one or more aldehydes disclosed herein. In some embodiments, the melamine is a substituted melamine. In certain embodiments, the melamine is replaced partially or totally with one or more phenol compounds disclosed herein. Some non-limiting examples of melamine-formaldehyde resins are described in Malcolm Stevens, “Polymer Chemistry: An Introduction,” Oxford University Press, New York, pp. 406-407 (1999), which is incorporated herein by reference.

In some embodiments, the condensation polymer disclosed herein contains reactive end groups comprising hydroxyl, carboxyl, amino, epoxy or a combination thereof. In certain embodiments, the condensation polymer disclosed herein is free of one or more end groups selected from hydroxyl, carboxyl, amino and epoxy. A skilled artisan can recognize that the reactive end groups of the condensation polymers disclosed herein can be unmodified or modified by any reaction or chemistry known in the literature. For example, the OH end group can be modified by reacting with a carboxylic acid to form an ester end group or with an epoxy halide compound, such as epichlorohydrin, to form an epoxy end group. In some embodiments, the condensation polymer disclosed herein contains two hydroxy end groups or at least one hydroxy end group. In certain embodiments, the condensation polymer disclosed herein contains two carboxyl end groups or at least one carboxyl end group. In some embodiments, the condensation polymer disclosed herein contains two amino end groups or at least one amino end group. In certain embodiments, the condensation polymer disclosed herein contains two epoxy end groups or at least one epoxy end group. In some embodiments, the condensation polymer disclosed herein contains at least one hydroxy end group and at least one carboxyl end group. In certain embodiments, the condensation polymer disclosed herein contains at least one amino end group and at least one carboxyl end group.

The polyfarnesene disclosed herein can be a farnesene homopolymer derived from a farnesene, a farnesene interpolymer derived from a farnesene and at least a vinyl monomer, or a combination thereof. In certain embodiments, the polyfarnesene is a farnesene homopolymer comprising units derived from at least one farnesene such as α-farnesene, β-farnesene or a combination thereof. In other embodiments, the polyfarnesene is a farnesene interpolymer comprising units derived from at least one farnesene and units derived from at least one copolymerizable vinyl monomer (e.g., styrene). In still further embodiments, the farnesene interpolymer is a random, block or alternating interpolymer. In still further embodiments, the farnesene interpolymer is a di-block, tri-block or other multi-block interpolymer.

In certain embodiments, the polyfarnesene comprises one or more polymer molecules having formula (A):

wherein n is an integer from 1 to about 500,000 or from 2 to about 500,000; m is an integer from 0 to about 500,000, from 1 to about 500,000 or from 2 to about 500,000; X is derived from a farnesene; and Y is derived from a vinyl monomer. In some embodiments, the polyfarnesene is a farnesene homopolymer wherein m is 0 and n is from 2 to about 500,000. In certain embodiments, the polyfarnesene is a farnesene interpolymer wherein n is from 1 or 2 to about 500,000 and m is from 1 or 2 to about 500,000.

In some embodiments, X has one or more of formulae (I)-(VIII):

-   wherein R¹ has formula (XI):

-   R² has formula (XII):

-   R³ has formula (XIII):

-    and -   R⁴ has formula (XIV):

In certain embodiments, Y has formula (IX):

-   wherein each of R⁵, R⁶, R⁷ and R⁸ is independently H, an organyl     group or a functional group. In some embodiments, each of R⁵, R⁶, R⁷     and R⁸ is independently H, alkyl, cycloalkyl, aryl, cycloalkenyl,     alkynyl, heterocyclyl, alkoxy, aryloxy, carboxy, alkoxycarbonyl,     aminocarbonyl, alkylaminocarbonyl, dialkylamino carbonyl, acyloxy,     nitrile or halo.

In general, the polyfarnesene comprising a mixture of polymer molecules, each of which has formula (A) wherein each of n and m independently has a specific value. The average and distribution of the n or m values disclosed herein depend on various factors such as the molar ratio of the starting materials, the reaction time and temperature, the presence or absence of a chain terminating agent, the amount of an initiator if there is any, and the polymerization conditions. The polyfarnesene of Formula (A) may include unreacted one or more monomers, although the concentrations of the one or more monomers would generally be small if not extremely small or undetectable. The extent of polymerization, as specified with n and m values, can affect the properties of the resulting polymer. In some embodiments, n is an integer from 1 to about 5,000, from 1 to about 10,000, from 1 to about 50,000, from 1 to about 100,000, from 1 to about 200,000, from 1 to about 500,000, from 2 to about 5,000, from 2 to about 10,000, from 2 to about 50,000, from 2 to about 100,000, from 2 to about 200,000, or from 2 to about 500,000; and m is an integer from 0 to about 5,000, from 0 to about 10,000, from 0 to about 50,000, from 0 to about 100,000, from 0 to about 200,000, from 0 to about 500,000, from 1 to about 5,000, from 1 to about 10,000, from 1 to about 50,000, from 1 to about 100,000, from 1 to about 200,000, or from 1 to about 500,000. In other embodiments, n is independently from about 1 to about 5000, from about 1 to about 2500, from about 1 to about 1000, from about 1 to about 500, from about 1 to about 100, from about 1 to about 50, from about 2 to about 5000, from about 2 to about 2500, from about 2 to about 1000, from about 2 to about 500, from about 2 to about 100 or from about 2 to about 50; and m is from 0 to about 5000, from 0 to about 2500, from 0 to about 1000, from 0 to about 500, from 0 to about 100, from 0 to about 50, from 1 to about 5000, from 1 to about 2500, from 1 to about 1000, from 1 to about 500, from 1 to about 100 or from 1 to about 50. A person of ordinary skill in the art will recognize that additional ranges of average n and m values are contemplated and are within the present disclosure.

In some embodiments, formula (X′) comprises two end groups as shown by the following formula:

where each of the asterisks (*) in the formula represents an end group which may or may not vary between different polymer molecules of the polyfarnesene depending on many factors such as the molar ratio of the starting materials, the presence or absence of a chain terminating agent, and the state of the particular polymerization process at the end of the polymerization step.

In some embodiments, the Xs and Ys of formula (A) or (A′) are linked in a substantially linear fashion. In other embodiments, the Xs and Ys of formula (A) or (A′) are linked in substantially branched fashion. In further embodiments, the Xs and Ys of formula (A) or (A′) are linked in substantially star-shaped fashion. In still further embodiments, each of the Xs and Ys independently forms at least a block along the polymer chain so as to provide a di-block, tri-block or multi-block farnesene interpolymer having at least one X block and at least one Y block. In still further embodiments, the Xs and Ys are randomly distributed along the polymer chain so as to provide a random farnesene interpolymer. In still further embodiments, the Xs and Ys are alternatively distributed along the polymer chain so as to provide an alternating farnesene interpolymer.

In some embodiments, the Xs of formula (A) or (A′) comprise one, two, three, four or more formulae selected from Formulae (I), (II), (III), (IV), (V), (VI), (VII) and (VIII) and stereoisomers thereof. In some embodiments, the Xs of formula (A) or (A′) comprise at least two formulae selected from Formulae (I), (II), (III), (IV), (V), (VI), (VII) and (VIII) and stereoisomers thereof. In some embodiments, the Xs of formula (A) or (A′) can be represented by the following formula: A_(x)B_(y) wherein each of x and y is at least 1, and wherein each of A and B independently has formula (I), (II), (III), (IV), (V), (VI), (VII) or (VIII) and A and B are different. In further embodiment, each of x and y is independently greater than 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40 or 50. In some embodiment, the As and Bs are linked in a substantially linear fashion. In other embodiments, the As and Bs are linked in a substantially branched or substantially star-shaped fashion. In certain embodiments, the As and Bs are randomly distributed. In other embodiments, the As and Bs are in two or more “segments” to provide a segmented structure, for example, AA---AA-BB---BB or AA---AA-BB---BB-AA---AA. In other embodiments, the As and Bs are alternatively distributed to provide an alternative structure, for example, A-B, A-B-A, A-B-A-B, A-B-A-B-A or the like.

In some embodiments, the Xs of formula (A) or (A′) comprise three or more units having three different formulae selected from formulae (I), (II), (III), (IV), (V), (VI), (VII) and (VIII), and stereoisomers thereof. In other embodiments, the Xs can be represented by the following formula: A_(x)B_(y)C_(z) wherein each of x, y and z is at least 1, and wherein each of A, B and C independently has formula (I), (II), (III), (IV), (V), (VI), (VII) or (VIII) and A, B and C are different. In further embodiment, each of x, y and z is independently greater than 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40 or 50. In some embodiment, the As, Bs and Cs are linked in a substantially linear fashion. In certain embodiment, the As, Bs and Cs are linked in a substantially branched or substantially star-shaped fashion. In other embodiments, the As, Bs and Cs are randomly distributed. In certain embodiments, the As, Bs and Cs are in three “segments” to provide an X having a segmented structure, for example, AA--A-BB--B-CC--C. In other embodiments, the As, Bs and Cs are alternatively distributed to provide an alternative structure, for example, A-B-C-A-B, A-B-C-A-B-C or the like.

In some embodiment, each of n and m of formula (A) or (A′) is independently greater than 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40 or 50. In some embodiment, the Xs and Ys are linked in a substantially linear fashion. In other embodiment, the Xs and Ys are linked in a substantially branched or substantially star-shaped fashion. In certain embodiments, the Xs and Ys are randomly distributed. In other embodiments, the Xs and Ys are in two or more blocks or segments to provide a block structure such as diblock or triblock structures, for example, XX---XX-YY---YY or XX---XX-YY---YY-X---XX or YY---YY-XX---XX-YY---YY. In other embodiments, the Xs and Ys are alternatively distributed along the farnesene interpolymer chain to provide a farnesene interpolymer having an alternative structure, for example, X-Y, X-Y-X, X-Y-X-Y, X-Y-X-Y-X or the like. In some embodiments, each X has formula A_(x)B_(y) or A_(x)B_(y)C_(z) as disclosed herein.

In certain embodiments, the farnesene interpolymer is derived from a farnesene and at least a vinyl monomer. In some embodiments, the amount of the farnesene in the farnesene interpolymer disclosed herein is greater than about 1.5 mole %, greater than about 2.0 mole %, greater than about 2.5 mole %, greater than about 5 mole %, greater than about 10 mole %, greater than about 15 mole %, or greater than about 20 mole %, based on the total amount of the farnesene interpolymer. In other embodiments, the amount of the farnesene in the farnesene interpolymer disclosed herein is less than about 90 mole %, less than about 80 mole %, less than about 70 mole %, less than about 60 mole %, less than about 50 mole %, less than about 40 mole %, or less than about 30 mole %, based on the total amount of the farnesene interpolymer.

In some embodiments, the amount of the vinyl monomer in the farnesene interpolymer disclosed herein is greater than about 1.5 mole %, greater than about 2.0 mole %, greater than about 2.5 mole %, greater than about 5 mole %, greater than about 10 mole %, greater than about 15 mole %, or greater than about 20 mole %, based on the total amount of the farnesene interpolymer. In other embodiments, the amount of the vinyl monomer in the farnesene interpolymer disclosed herein is less than about 90 mole %, less than about 80 mole %, less than about 70 mole %, less than about 60 mole %, less than about 50 mole %, less than about 40 mole %, or less than about 30 mole %, based on the total amount of the farnesene interpolymer.

In certain embodiments, the mole percent ratio of the farnesene to the vinyl monomer (i.e., the mole percent ratio of X to Y) in the farnesene interpolymer disclosed herein is from about 1:5 to about 100:1. In other embodiments, the mole percent ratio of X to Y is from about 1:4 to about 100:1; from about 1:3.5 to about 100:1, from about 1:3 to about 100:1, from about 1:2.5 to about 100:1, or from about 1:2 to about 100:1. In some embodiments, m is 1 or greater, the mole percent ratio of X to Y is from about 1:4 to about 100:1

In certain embodiments, the amount of formula (I) or (II) or a combination thereof in the polyfarnesene disclosed herein is at most about 85 wt. %, at most about 80 wt. %, at most about 70 wt. %, at most about 60 wt. %, or at most about 50 wt. %, based on the total weight of the polyfarnesene. In other embodiments, the amount of formula (III) or (IV) in the polyfarnesene disclosed herein is at least about 10 wt. %, at least about 15 wt. %, at least about 20 wt. %, at least about 25 wt. %, at least about 30 wt. %, at least about 40 wt. %, at least about 50 wt. %, at least about 60 wt. %, at least about 70 wt. %, at least about 75 wt. %, at least about 80 wt. %, at least about 85 wt. %, at least about 90 wt. %, at least about 95 wt. %, or at least about 99 wt. %, based on the total weight of the polyfarnesene. In further embodiments, the amount of formula (II) in the polyfarnesene disclosed herein is from about 1 wt. % to about 99 wt. %, from about 5 wt. % to about 99 wt. %, from about 10 wt. % to about 99 wt. %, or from about 15 wt. % to about 99 wt. %, based on the total weight of the polyfarnesene. In still further embodiments, the amount of formula (IV) in the polyfarnesene disclosed herein is at most about 0.1 wt. %, at most about 0.5 wt. %, at most about 1 wt. %, at most about 2 wt. %, or at most about 3 wt. %, based on the total weight of the polyfarnesene. In some embodiments, the polyfarnesene disclosed herein is substantially free of formula (I), (II), (III) or (IV).

In certain embodiments, the amount of formula (V), (VI), (VII) or (VIII) in the polyfarnesene disclosed herein is at most about 1 wt. %, at most about 5 wt. %, at most about 10 wt. %, at most about 20 wt. %, at most about 30 wt. %, at most about 40 wt. %, at most about 50 wt. %, at most about 60 wt. %, at most about 70 wt. %, at most about 80 wt. %, or at most about 90 wt. %, based on the total weight of the polyfarnesene. In other embodiments, the amount of formula (V), (VI), (VII) or (VIII) in the polyfarnesene disclosed herein is at least about 1 wt. %, at least about 2 wt. %, at least about 3 wt. %, at least about 5 wt. %, at least about 10 wt. %, at least about 20 wt. %, at least about 30 wt. %, at least about 40 wt. %, at least about 50 wt. %, at least about 60 wt. %, based on the total weight of the polyfarnesene. In further embodiments, the amount of formula (V), (VI), (VII) or (VIII) in the polyfarnesene disclosed herein is from about 1 wt. % to about 99 wt. %, from about 5 wt. % to about 99 wt. %, from about 10 wt. % to about 99 wt. %, or from about 15 wt. % to about 99 wt. %, based on the total weight of the polyfarnesene. In some embodiments, the polyfarnesene disclosed herein is substantially free of formula (V), (VI), (VII) or (VIII).

Any compound containing a vinyl group, i.e., —CH═CH₂, that is copolymerizable with farnesene can be used as a vinyl monomer for making the farnesene interpolymer disclosed herein. Useful vinyl monomers disclosed herein include ethylene, i.e., CH₂═CH₂. In certain embodiments, the vinyl monomer has formula (XV):

where each of R⁵, R⁶, R⁷ and R⁸ is independently H, an organyl group or a functional group.

In some embodiments, at least one of R⁵, R⁶, R⁷ and R⁸ of formula (IX) or (XV) is an organyl group. In further embodiments, the organyl group is hydrocarbyl, substituted hydrocarbyl, heterocyclyl or substituted heterocyclyl. In certain embodiments, each of R⁵, R⁶, R⁷ and R⁸ of formula (IX) or (XV) is independently H, alkyl, cycloalkyl, aryl, alkenyl, cycloalkenyl, alkynyl, heterocyclyl, alkoxy, aryloxy, carboxy, alkoxycarbonyl, aminocarbonyl, alkylaminocarbonyl, dialkylaminocarbonyl, acyloxy, nitrile or halo. In other embodiments, each of R⁵, R⁶, R⁷ and R⁸ of formula (IX) or (XV) is independently H, alkyl, cycloalkyl, aryl, cycloalkenyl, alkynyl, heterocyclyl, alkoxy, aryloxy, carboxy, alkoxycarbonyl, aminocarbonyl, alkylaminocarbonyl, dialkylaminocarbonyl, acyloxy, nitrile or halo. In certain embodiments, R⁵ of formula (IX) or (XV) is aryl; and each of R⁶, R⁷ and R⁸ is H. In further embodiments, R⁵ of formula (IX) or (XV) is phenyl; and each of R⁶, R⁷ and R⁸ is H.

In certain embodiments, at least one of R⁵, R⁶, R⁷ and R⁸ of formula (IX) or (XV) is H. In other embodiments, each of R⁵, R⁶, R⁷ and R⁸ of formula (IX) or (XV) is H. In further embodiments, R⁵ of formula (IX) or (XV) is hydrocarbyl; and each of R⁶, R⁷ and R⁸ is H. In still further embodiments, the hydrocarbyl is alkyl, cycloalkyl or aryl. In still further embodiments, none of R⁵, R⁶, R⁷ and R⁸ of formula (IX) or (XV) is or comprises alkenyl, cycloalkenyl or alkynyl. In still further embodiments, none of R⁵, R⁶, R⁷ and R⁸ of formula (IX) or (XV) is or comprises a hydrocarbyl, substituted hydrocarbyl, heterocyclyl or substituted heterocyclyl.

In certain embodiments, at least one of R⁵, R⁶, R⁷ and R⁸ of formula (IX) or (XV) is a functional group containing halo, O, N, S, P or a combination thereof. Some non-limiting examples of suitable functional groups include hydroxy, alkoxy, aryloxy, nitro, thiol, thioether, imine, cyano, amido, phosphonato (—P(═O)(O-alkyl)₂, —P(═O)(O-aryl)₂, or —P(═O)(O-alkyl))O-aryl), phosphinato (—P(═O)(O-alkyl)alkyl, —P(═O)(O-aryl)alkyl, —P(═O)(O-alkyl)aryl, or —P(═O)(O-aryl)aryl), carboxyl, anhydride, thiocarbonyl, sulfonyl (—S(═O)₂alkyl, or —S(═O)₂aryl), sulfonamide (—SO₂NH₂, —SO₂NH(alkyl), —SO₂NH(aryl), —SO₂N(alkyl)₂, —SO₂N(aryl)₂, or —SO₂N(aryl)(alkyl)), ketone, aldehyde, ester, oxo, epoxy, glycidyl, amino (e.g., primary, secondary or tertiary amino such as —NH₂, —NH(alkyl), —N(alkyl)₂, —NH(aryl), —N(alkyl)(aryl), —N(aryl)₂,), —CO₂CH₃, —CONH₂, —OCH₂CONH₂, —OCHF₂, —OCF₃, —CHO, —CO(alkyl), —CO(aryl), —CO₂(alkyl), or —CO₂(aryl). In some embodiments, the functional group is or comprises hydroxy, carboxyl, amino, epoxy, glycidyl, anhydride, alkoxycarbonyl, aminocarbonyl, alkylaminocarbonyl, dialkylaminocarbonyl or acyloxy. In other embodiments, none of R⁵, R⁶, R⁷ and R⁸ of formula (IX) or (XV) is or comprises a functional group. In other embodiments, none of R⁵, R⁶, R⁷ and R⁸ of formula (IX) or (XV) is or comprises hydroxy, carboxyl, amino, epoxy, glycidyl, anhydride, alkoxycarbonyl, aminocarbonyl, alkylaminocarbonyl, dialkylaminocarbonyl or acyloxy.

In some embodiments, the vinyl monomer is a substituted or unsubstituted olefin such as ethylene or styrene, vinyl halide, vinyl ether, acrylonitrile, acrylic ester, methacrylic ester, acrylamide, methacrylamide or a combination thereof. In other embodiments, the vinyl monomer is ethylene, an α-olefin or a combination thereof. Some non-limiting examples of suitable α-olefins include styrene, propylene, 1-butene, 1-hexene, 1-octene, 4-methyl-1-pentene, norbornene, 1-decene, 1,5-hexadiene and combinations thereof.

In some embodiments, the vinyl monomer is an aryl such as styrene, α-methyl styrene, or di-vinyl benzene. Additional examples include the functionalized vinyl aryls such as those disclosed by U.S. Pat. No. 7,041,761 which is incorporated herein by reference.

In some embodiments, the farnesene interpolymers disclosed herein are derived from at least one farnesene and at least one olefin monomer. An olefin refers to an unsaturated hydrocarbon-based compound with at least one carbon-carbon double bond. In certain embodiments, the olefin is a conjugated diene. Depending on the selection of catalysts, any olefin may be used in embodiments of the invention. Some non-limiting examples of suitable olefins include C₂₋₂₀ aliphatic and C₈₋₂₀ aromatic compounds containing vinylic unsaturation, as well as cyclic compounds, such as cyclobutene, cyclopentene, dicyclopentadiene, and norbornene, including but not limited to, norbornene substituted in the 5 and 6 position with C₁₋₂₀ hydrocarbyl or cyclohydrocarbyl groups. Other non-limiting examples of suitable olefins include mixtures of such olefins as well as mixtures of such olefins with C₄₋₄₀ diolefin compounds.

Some non-limiting examples of suitable olefin or α-olefin monomers include styrene, ethylene, propylene, isobutylene, 1-butene, 1-pentene, 1-hexene, 1-heptene, 1-octene, 1-nonene, 1-decene, and 1-dodecene, 1-tetradecene, 1-hexadecene, 1-octadecene, 1-eicosene, 3-methyl-1-butene, 3-methyl-1-pentene, 4-methyl-1-pentene, 4,6-dimethyl-1-heptene, 4-vinylcyclohexene, vinylcyclohexane, norbornadiene, ethylidene norbornene, cyclopentene, cyclohexene, dicyclopentadiene, cyclooctene, C₄₋₄₀ dienes, including but not limited to 1,3-butadiene, 1,3-pentadiene, 1,4-hexadiene, 1,5-hexadiene, 1,7-octadiene, 1,9-decadiene, other C₄₋₄₀ α-olefins, and the like. In certain embodiments, the olefin monomer is propylene, 1-butene, 1-pentene, 1-hexene, 1-octene or a combination thereof.

The farnesene interpolymers disclosed herein may derived from a farnesene and styrene. The farnesene interpolymers may further comprise at least one C₂₋₂₀ olefin, at least one C₄₋₁₈ diolefin, at least one alkenylbenzene or a combination thereof. Suitable unsaturated comonomers useful for polymerizing with farnesene include, for example, ethylenically unsaturated monomers, polyenes such as conjugated or nonconjugated dienes, alkenylbenzenes, and the like. Examples of such comonomers include ethylene, C₂₋₂₀ olefins such as propylene, isobutylene, 1-butene, 1-hexene, 1-pentene, 4-methyl-1-pentene, 1-heptene, 1-octene, 1-nonene, 1-decene, and the like. Other suitable monomers include styrene, halo- or alkyl-substituted styrenes, vinylbenzocyclobutane, 1,4-hexadiene, 1,7-octadiene, and cycloalkenes such as cyclopentene, cyclohexene and cyclooctene.

Some suitable non-conjugated diene monomers can be a straight chain, branched chain or cyclic hydrocarbon diene having from 6 to 15 carbon atoms. Some non-limiting examples of suitable non-conjugated dienes include straight chain acyclic dienes, such as 1,4-hexadiene, 1,6-octadiene, 1,7-octadiene, 1,9-decadiene, branched chain acyclic dienes, such as 5-methyl-1,4-hexadiene; 3,7-dimethyl-1,6-octadiene; 3,7-dimethyl-1,7-octadiene and mixed isomers of dihydromyricene and dihydroocinene, single ring alicyclic dienes, such as 1,3-cyclopentadiene; 1,4-cyclohexadiene; 1,5-cyclooctadiene and 1,5-cyclododecadiene, and multi-ring alicyclic fused and bridged ring dienes, such as tetrahydroindene, methyl tetrahydroindene, dicyclopentadiene, bicyclo-(2,2,1)-hepta-2,5-diene; alkenyl, alkylidene, cycloalkenyl and cycloalkylidene norbornenes, such as 5-methylene-2-norbornene (MNB); 5-propenyl-2-norbornene, 5-isopropylidene-2-norbornene, 5-(4-cyclopentenyl)-2-norbornene, 5-cyclohexylidene-2-norbornene, 5-vinyl-2-norbornene, and norbornadiene. Of the dienes typically used to prepare EPDMs, the particularly preferred dienes are 1,4-hexadiene (HD), 5-ethylidene-2-norbornene (ENB), 5-vinylidene-2-norbornene (VNB), 5-methylene-2-norbornene (MNB), and dicyclopentadiene (DCPD). In certain embodiments, the diene is 5-ethylidene-2-norbornene (ENB) or 1,4-hexadiene (HD). In other embodiments, the farnesene interpolymers are not derived from a polyene such as dienes, trienes, tetraenes and the like.

In some embodiments, the farnesene interpolymers are interpolymers of farnesene, styrene, and a C₂₋₂₀ olefin. Some non-limiting examples of suitable olefins include ethylene, propylene, isobutylene, 1-butene, 1-pentene, 1-hexene, 4-methyl-1-pentene, and 1-octene. In some embodiments, the farnesene interpolymers disclosed herein are not derived from ethylene. In some embodiments, the farnesene interpolymers disclosed herein are not derived from one or more C₂₋₂₀ olefins.

In certain embodiments, the vinyl monomer does not comprise a terpene. In other embodiments, the vinyl monomer does not comprise a terpene selected from isoprene, dipentene, α-pinene, β-pinene, terpinolene, limonene (dipentene), terpinene, thujene, sabinene, 3-carene, camphene, cadinene, caryophyllene, myrcene, ocimene, cedrene, bisalbone, bisalbone, bisalbone, zingiberene, humulene, citronellol, linalool, geraniol, nerol, ipsenol, terpineol, D-terpineol-(4), dihydrocarveol, nerolidol, farnesol, eudesmol, citral, D-citronellal, carvone, D-pulegone, piperitone, carvenone, bisabolene, selinene, santalene, vitamin A, abietic acid or a combination thereof. In further embodiments, the vinyl monomer does not comprise an isoprene.

In some embodiments, the farnesene interpolymer disclosed herein is a random interpolymer. In other embodiments, the farnesene interpolymer disclosed herein is a random interpolymer wherein the Xs and the Ys are randomly distributed. In certain embodiments, the farnesene interpolymer disclosed herein is an alternating interpolymer. In other embodiments, the farnesene interpolymer disclosed herein is an alternating interpolymer wherein the Xs and the Ys are alternatively distributed. In some embodiments, the farnesene interpolymer is a block interpolymer having one or more first blocks comprising the Xs and one or more second blocks comprising the Ys. In other embodiments, there are one first block comprising the Xs and two second blocks comprising the Ys and wherein the first block is between the two second blocks. In further embodiments, the Ys are derived from styrene. In some embodiments, the farnesene block interpolymer is a polystyrene-polyfarnesene di-block polyfarnesene, polystyrene-polyfarnesene-polystyrene tri-block polyfarnesene or a combination thereof.

In some embodiments, the sum of m and n of formula (A) or (A′) is greater than about 50, greater than about 100, greater than about 150, greater than about 200, greater than about 250, greater than about 300, greater than about 500, greater than about 750, greater than about 1000, or greater than about 2000.

In certain embodiments, the number-average molecular weight (M_(n)), weight-average molecular weight (M_(w)), or viscosity-average molecular weight (M_(z)) of the polyfarnesene disclosed herein is greater than about 60,000 daltons, greater than about 100,000 daltons, greater than 200,000 daltons, greater than 300,000 daltons, greater than about 500,000 daltons, greater than 750,000 daltons, greater than 1,000,000 daltons, greater than 1,500,000 daltons, or greater than 2,000,000 daltons. In other embodiments, the M_(n), M_(w) or M_(z) of the polyfarnesene disclosed herein is less than about 10,000,000 daltons, less than 5,000,000 daltons, less than 1,000,000 daltons, less than about 750,000 daltons, or less than 500,000 daltons.

In some embodiments, the polyfarnesene disclosed herein has at least a glass transition temperature (T_(g)) of less than −55° C., less than −60° C., less than −65° C., less than −70° C., or less than −75° C., as measured according to ASTM D7426-08 titled “Standard Test Method for Assignment of the DSC Procedure for Determining T _(g) of a Polymer or an Elastomeric Compound,” which is incorporated herein by reference.

Any catalyst that can polymerize or copolymerize farnesene can be used for making the polyfarnesenes disclosed herein. Some non-limiting examples of suitable catalysts include organolithium reagents, Ziegler-Natta catalysts, Kaminsky catalysts and other metallocene catalysts. In some embodiments, the catalyst is a Ziegler-Natta catalyst, a Kaminsky catalyst, a metallocene catalyst or a combination thereof.

In some embodiments, the catalyst further comprises a cocatalyst. In further embodiments, the cocatalyst is a hydride, alkyl or aryl of a metal or a combination thereof. In still further embodiments, the metal is aluminum, lithium, zinc, tin, cadmium, beryllium or magnesium.

In some embodiments, the catalyst is an organolithium reagent. Any organolithium reagent that can act as a catalyst to polymerize olefins can be used herein. Some non-limiting examples of suitable organolithium reagents include n-butyllithium, sec-butyllithium or tert-butyllithium. Some non-limiting examples of suitable Lewis bases include TMEDA, PMDTA or sparteine. Some organo lithium reagents are disclosed in Zvi Rappoport et al., “The Chemistry of Organolithium Compounds,” Part 1 (2004) and Vol. 2 (2006), both of which are incorporated herein by reference.

In some embodiments, the catalyst is a mixture of an organolithium reagent and a Lewis base. Any Lewis base that can deaggregate organolithium reagents, making them more soluble and more reactive, can be used herein. An aggregated organolithium reagent generally has one lithium coordinating to more than one carbon atom and one carbon coordinating to more than one lithium atom. Some non-limiting examples of suitable Lewis bases include 1,2-bis(dimethylamino)ethane (also known as tetramethylethylenediamine or TMEDA), N,N,N′,N′,N″-pentamethyldiethylenetriamine (PMDTA), sparteine and combinations thereof.

In some embodiments, the catalyst is a Ziegler-Natta catalyst. Generally, Ziegler-Natta catalysts can be heterogeneous or homogeneous. In some embodiments, the Ziegler-Natta catalyst used for polymerizing the polyfarnesenes disclosed herein is a heterogeneous Ziegler-Natta catalyst. Some useful Ziegler-Natta catalysts are disclosed in J. Boor, “Ziegler-Natta Catalysts and Polymerizations,” Saunders College Publishing, pp. 1-687 (1979); and Malcolm P. Stevens, “Polymer Chemistry, an Introduction,” Third Edition, Oxford University Press, pp. 236-245 (1999), both of which are incorporated herein by reference.

Heterogeneous Ziegler-Natta catalysts generally comprise (1) a transition metal compound comprising an element from groups IV to VIII; and (2) an organometallic compound comprising a metal from groups I to III of the periodic table. The transition metal compound is referred as the catalyst while the organometallic compound is regarded as the cocatalyst or activator. The transition metal compound generally comprises a metal and one or more anions and ligands. Some non-limiting examples of suitable metals include titanium, vanadium, chromium, molybdenum, zirconium, iron and cobalt. Some non-limiting examples of suitable anions or ligands include halides, oxyhalides, alkoxy, acetylacetonyl, cyclopentadienyl, and phenyl.

Any cocatalyst or activator that can ionize the organometallic complex to produce an active olefin polymerization catalyst can be used herein. Generally, the organometallic cocatalysts are hydrides, alkyls, or aryls of metals, such as aluminum, lithium, zinc, tin, cadmium, beryllium, and magnesium. Some non-limiting examples of suitable cocatalysts include alumoxanes (methyl alumoxane (MAO), PMAO, ethyl alumoxane, diisobutyl alumoxane), alkylaluminum compounds (trimethylaluminum, triethylaluminum, diethyl aluminum chloride, trimethylaluminum, triisobutylaluminum, trioctylaluminum), diethylzinc, di(i-butyl)zinc, di(n-hexyl)zinc, and ethylzinc (t-butoxide) and the like. Other suitable cocatalysts include acid salts that contain non-nucleophilic anions. These compounds generally consist of bulky ligands attached to boron or aluminum. Some non-limiting examples of such compounds include lithium tetrakis(pentafluorophenyl)borate, lithium tetrakis(pentafluorophenyl)aluminate, anilinium tetrakis(pentafluorophenyl)borate, and the like. Some non-limiting examples of suitable cocatalysts also include organoboranes, which include boron and one or more alkyl, aryl, or aralkyl groups. Other non-limiting examples of suitable cocatalysts include substituted and unsubstituted trialkyl and triarylboranes such as tris(pentafluorophenyl)borane, triphenylborane, tri-n-octylborane, and the like. These and other suitable boron-containing cocatalysts or activators are described in U.S. Pat. Nos. 5,153,157, 5,198,401, and 5,241,025, both of which are incorporated herein by reference.

In certain embodiments, the Ziegler-Natta catalyst can be impregnated on a support material. Some suitable support materials are disclosed in Malcolm P. Stevens, “Polymer Chemistry, an Introduction,” Third Edition, Oxford University Press, p. 251 (1999), which is incorporated herein by reference.

The support material is generally a material inert or substantially inert to olefin polymerization reactions. Non-limiting examples of suitable support materials include MgCl₂, MgO, alumina such as activated alumina and microgel alumina, silica, magnesia, kieselguhr, fuller's earth, clays, alumina silicates, porous rare earth halides and oxylalides, and combinations thereof. The support material can have a surface area between about 5 m²/g and about 450 m²/g, as determined by the BET (Brunauer-Emmet-Teller) method of measuring surface area, as described by S. Brunauer, P. H. Emmett, and E. Teller, Journal of the American Chemical Society, 60, 309 (1938), which is incorporated herein by reference. In some embodiments, the surface area of the support material is between about 10 m²/g and about 350 m²/g. In further embodiments, the surface area of the support material is between about 25 m²/g and about 300 m²/g.

The support material can have an average particle size ranging from about 20 to about 300 microns, from about 20 to about 250 microns, from about 20 to about 200 microns, from about 20 to about 150 microns, from about 20 to about 120 microns, from about 30 to about 100 microns, or from about 30 to about 90 microns. The compacted or tamped bulk density of the support material can vary between about 0.6 and about 1.6 g/cc, between about 0.7 and about 1.5 g/cc, between about 0.8 and about 1.4 g/cc, or between about 0.9 and about 1.3 g/cc.

In certain embodiments, the catalyst used herein is or comprises a Kaminsky catalyst, also known as homogeneous Ziegler-Natta catalyst. The Kaminsky catalyst can be used to produce polyolefins such as the polyfarnesenes disclosed herein with unique structures and physical properties. Some Kaminsky catalysts or homogeneous Ziegler-Natta catalysts are disclosed in Malcolm P. Stevens, “Polymer Chemistry, an Introduction,” Third Edition, Oxford University Press, pp. 245-251 (1999); and John Scheirs and Walter Kaminsky, “Metallocene-Based Polyolefins: Preparation, Properties, and Technology,” Volume 1, Wiley (2000), both of which are incorporated herein by reference.

In some embodiments, the Kaminsky catalyst suitable for making the polyfarnesene disclosed herein comprises a transition-metal atom sandwiched between ferrocene ring structures. In other embodiments, the Kaminsky catalyst can be represented by the formula Cp₂MX₂, where M is a transition metal (e.g., Zr, Ti or Hf); X is halogen (e.g., Cl), alkyl or a combination thereof; and Cp is a ferrocenyl group. In further embodiments, the Kaminsky catalyst has formula (XXVI):

wherein Z is an optional divalent bridging group, usually C(CH₃)₂, Si(CH₃)₂, or CH₂CH₂; R is H or alkyl; M is a transition metal (e.g., Zr, Ti or Hf); X is halogen (e.g., Cl), alkyl or a combination thereof. Some non-limiting examples of Kaminsky catalysts have formulae (XXVII) to (XXIX):

wherein M is Zr, Hf or Ti.

In some embodiments, a cocatalyst is used with the Kaminsky catalyst. The cocatalyst may be any of the cocatalyst disclosed herein. In certain embodiments, the cocatalyst is methylaluminoxane (MAO). MAO is an oligomeric compound having a general formula (CH₃AlO)_(n), where n is from 1 to 10. MAO may play several roles: it alkylates the metallocene precursor by replacing chlorine atoms with methyl groups; it produces the catalytic active ion pair Cp₂MCH₃ ⁺/MAO⁻, where the cationic moiety is considered responsible for polymerization and MAO⁻ acts as weakly coordinating anion. Some non-limiting examples of MAO include formulae (XXX) to (XXXI):

In certain embodiments, the catalyst for making the polyfarnesene disclosed herein is or comprises a metallocene catalyst. Some metallocene catalysts are disclosed in Tae Oan Ahn et al., “Modification of a Ziegler-Natta catalyst with a metallocene catalyst and its olefin polymerization behavior,” Polymer Engineering and Science, 39(7), p. 1257 (1999); and John Scheirs and Walter Kaminsky, “Metallocene-Based Polyolefins: Preparation, Properties, and Technology,” Volume 1, Wiley (2000), both of which are incorporated herein by reference.

In other embodiments, the metallocene catalyst comprises complexes with a transition metal centre comprising a transition metal, such as Ni and Pd, and bulky, neutral ligands comprising alpha-diimine or diketimine. In further embodiments, the metallocene catalyst has formula (XXXII):

wherein M is Ni or Pd.

In some embodiments, the catalyst used herein is or comprises a metallocene catalyst bearing mono-anionic bidentate ligands. A non-limiting example of such a metallocene catalyst has structure (XXXIII):

In other embodiments, the catalyst used herein is or comprises a metallocene catalyst comprising iron and a pyridyl is incorporated between two imine groups giving a tridentate ligand. A non-limiting example of such a metallocene catalyst has structure (XXXIV):

In some embodiments, the catalyst used herein is or comprises a metallocene catalyst comprising a salicylimine catalyst system based on zirconium. A non-limiting example of such a metallocene catalyst has structure (XXXV):

In some embodiments, the farnesene homopolymer disclosed herein is prepared by a process comprising the steps of:

-   -   (a) making a farnesene from a simple sugar or non-fermentable         carbon source by using a microorganism; and     -   (b) polymerizing the farnesene in the presence of a catalyst         disclosed herein.

In certain embodiments, the polyfarnesene disclosed herein is prepared by a process comprising the steps of:

-   -   (a) making a farnesene from a simple sugar or non-fermentable         carbon source by using a microorganism; and     -   (b) copolymerizing the farnesene and at least one vinyl monomer         in the presence of a catalyst disclosed herein.

In some embodiments, the polyfarnesene disclosed herein is prepared by polymerizing β-farnesene in the presence of a catalyst, wherein the amount of the cis-1,4-microstructure in the polyfarnesene is at most about 80 wt. %, at most about 75 wt. %, at most about 70 wt. %, at most about 65 wt. %, or at most about 60 wt. %, based on the total weight of the polyfarnesene. In some embodiments, the β-farnesene is copolymerized with a vinyl monomer to form a farnesene copolymer. In other embodiments, the vinyl monomer is styrene. In further embodiments, the farnesene copolymer is a block copolymer.

In certain embodiments, the polyfarnesene disclosed herein is prepared by polymerizing an α-farnesene in the presence of a catalyst. wherein the amount of the cis-1,4-microstructure in the polyfarnesene is from about 1 wt. % to about 99 wt. %, from about 10 wt. % to about 99 wt. %, from about 20 wt. % to about 99 wt. %, from about 30 wt. % to about 99 wt. %, from about 40 wt. % to about 99 wt. %, from about 50 wt. % to about 99 wt. %, from about 1 wt. % to about 99 wt. %, from about 1 wt. % to about 90 wt. %, from about 1 wt. % to about 80 wt. %, from about 1 wt. % to about 70 wt. %, or from about 1 wt. % to about 60 wt. %, based on the total weight of the polyfarnesene. In some embodiments, the α-farnesene is copolymerized with a vinyl monomer to form a farnesene copolymer. In other embodiments, the vinyl monomer is styrene. In further embodiments, the farnesene copolymer is a block copolymer.

In some embodiments, the polyfarnesene disclosed herein can be hydrogenated partially or completely by any hydrogenating agent known to a skilled artisan. For example, a saturated polyfarnesene can be prepared by (a) polymerizing a farnesene disclosed herein in the presence of a catalyst disclosed herein to form a polyfarnesene; and (b) hydrogenating at least a portion of the double bonds in the polyfarnesene in the presence of a hydrogenation reagent. In some embodiments, the farnesene is copolymerized with a vinyl monomer disclosed herein to form a farnesene copolymer. In other embodiments, the vinyl monomer is styrene. In further embodiments, the farnesene copolymer is a block copolymer. In still further embodiments, the farnesene is α-farnesene or β-farnesene or a combination thereof.

In certain embodiments, the hydrogenation reagent is hydrogen in the presence of a hydrogenation catalyst. In some embodiments, the hydrogenation catalyst is Pd, Pd/C, Pt, PtO₂, Ru(PPh₃)₂Cl₂, Raney nickel or a combination thereof. In one embodiment, the catalyst is a Pd catalyst. In another embodiment, the catalyst is 5% Pd/C. In a further embodiment, the catalyst is 10% Pd/C in a high pressure reaction vessel and the hydrogenation reaction is allowed to proceed until completion. Generally, after completion, the reaction mixture can be washed, concentrated, and dried to yield the corresponding hydrogenated product. Alternatively, any reducing agent that can reduce a C═C bond to a C—C bond can also be used. For example, the polyfarnesene can be hydrogenated by treatment with hydrazine in the presence of a catalyst, such as 5-ethyl-3-methyllumiflavinium perchlorate, under an oxygen atmosphere to give the corresponding hydrogenated products. The reduction reaction with hydrazine is disclosed in Imada et al., J. Am. Chem. Soc., 127, 14544-14545 (2005), which is incorporated herein by reference.

In some embodiments, at least a portion of the C═C bonds of the polyfarnesene disclosed herein is reduced to the corresponding C—C bonds by hydrogenation in the presence of a catalyst and hydrogen at room temperature. In other embodiments, at least a portion of the C═C bonds of one or more of formulae (I′)-(III′), (V′)-(VII′), and (XI)-(XIV) and stereoisomers thereof is reduced to the corresponding C—C bonds by hydrogenation in the presence of a catalyst and hydrogen at room temperature. In further embodiments, the hydrogenation catalyst is 10% Pd/C.

In certain embodiments, the vinyl monomer is styrene. In some embodiments, the farnesene is α-farnesene or β-farnesene or a combination thereof. In other embodiments, the farnesene is prepared by using a microorganism. In further embodiments, the farnesene is derived from a simple sugar or non-fermentable carbon source.

Farnesene

The farnesene can be derived from any source or prepared by any method known to a skilled artisan. In some embodiments, the farnesene is derived from a chemical source (e.g., petroleum or coal) or obtained by a chemical synthetic method. In other embodiments, the farnesene is prepared by fractional distillation of petroleum or coal tar. In further embodiments, the farnesene is prepared by any known chemical synthetic method. One non-limiting example of suitable chemical synthetic method includes dehydrating nerolidol with phosphoryl chloride in pyridine as described in the article by Anet E. F. L. J., “Synthesis of (E,Z)-α-,(Z,Z)-α-, and (Z)-β-farnesene,” Aust. J. Chem., 23(10), 2101-2108 (1970), which is incorporated herein by reference.

In some embodiments, the farnesene can be obtained or derived from naturally occurring terpenes that can be produced by a wide variety of plants, such as Copaifera langsdorfii, conifers, and spurges; insects, such as swallowtail butterflies, leaf beetles, termites, and pine sawflies; and marine organisms, such as algae, sponges, corals, mollusks, and fish.

Copaifera langsdorfii or Copaifera tree is also known as the diesel tree and kerosene tree. It has many names in local languages, including kupa'y, cabismo, and copaúva. Copaifera tree may produce a large amount of terpene hydrocarbons in its wood and leaves. Generally, one Copaifera tree can produce from about 30 to about 40 liters of terpene oil per year.

Terpene oils can also be obtained from conifers and spurges. Conifers belong to the plant division Pinophyta or Coniferae and are generally cone-bearing seed plants with vascular tissue. The majority of conifers are trees, but some conifers can be shrubs. Some non-limiting examples of suitable conifers include cedars, cypresses, douglas-firs, firs, junipers, kauris, larches, pines, redwoods, spruces, and yews. Spurges, also known as Euphorbia, are a very diverse worldwide genus of plants, belonging to the spurge family (Euphorbiaceae). Consisting of about 2160 species, spurges are one of the largest genera in the plant kingdom.

The farnesene is a sesquiterpene which are part of a larger class of compound called terpenes. A large and varied class of hydrocarbons, terpenes include hemiterpenes, monoterpenes, sesquiterpenes, diterpenes, sesterterpenes, triterpenes, tetraterpenes, and polyterpenes. As a result, the farnesene can be isolated or derived from terpene oils for use in the present invention.

In certain embodiments, the farnesene is derived from a biological source. In other embodiments, the farnesene can be obtained from a readily available, renewable carbon source. In further embodiments, the farnesene is prepared by contacting a cell capable of making a farnesene with a carbon source under conditions suitable for making the farnesene.

Any carbon source that can be converted into one or more isoprenoid compounds can be used herein. In some embodiments, the carbon source is a sugar or a non-fermentable carbon source. The sugar can be any sugar known to those of skill in the art. In certain embodiments, the sugar is a monosaccharide, disaccharide, polysaccharide or a combination thereof. In other embodiments, the sugar is a simple sugar (a monosaccharide or a disaccharide). Some non-limiting examples of suitable monosaccharides include glucose, galactose, mannose, fructose, ribose and combinations thereof. Some non-limiting examples of suitable disaccharides include sucrose, lactose, maltose, trehalose, cellobiose and combinations thereof. In still other embodiments, the simple sugar is sucrose. In certain embodiments, the bioengineered fuel component can be obtained from a polysaccharide. Some non-limiting examples of suitable polysaccharides include starch, glycogen, cellulose, chitin and combinations thereof.

The sugar suitable for making the farnesene can be found in a wide variety of crops or sources. Some non-limiting examples of suitable crops or sources include sugar cane, bagasse, miscanthus, sugar beet, sorghum, grain sorghum, switchgrass, barley, hemp, kenaf, potatoes, sweet potatoes, cassaya, sunflower, fruit, molasses, whey or skim milk, corn, stover, grain, wheat, wood, paper, straw, cotton, many types of cellulose waste, and other biomass. In certain embodiments, the suitable crops or sources include sugar cane, sugar beet and corn. In other embodiments, the sugar source is cane juice or molasses.

A non-fermentable carbon source is a carbon source that cannot be converted by the organism into ethanol. Some non-limiting examples of suitable non-fermentable carbon sources include acetate and glycerol.

In certain embodiments, the farnesene can be prepared in a facility capable of biological manufacture of C₁₅ isoprenoids. The facility can comprise any structure useful for preparing the C₁₅ isoprenoids, such as α-farnesene, β-farnesene, nerolidol or farnesol, using a microorganism. In some embodiments, the biological facility comprises one or more of the cells disclosed herein. In other embodiments, the biological facility comprises a cell culture comprising at least a C₁₅ isoprenoid in an amount of at least about 1 wt. %, at least about 5 wt. %, at least about 10 wt. %, at least about 20 wt. %, or at least about 30 wt. %, based on the total weight of the cell culture. In further embodiments, the biological facility comprises a fermentor comprising one or more cells described herein.

Any fermentor that can provide cells or bacteria a stable and optimal environment in which they can grow or reproduce can be used herein. In some embodiments, the fermentor comprises a culture comprising one or more of the cells disclosed herein. In other embodiments, the fermentor comprises a cell culture capable of biologically manufacturing farnesyl pyrophosphate (FPP). In further embodiments, the fermentor comprises a cell culture capable of biologically manufacturing isopentenyl diphosphate (IPP). In certain embodiments, the fermentor comprises a cell culture comprising at least a C₁₅ isoprenoid in an amount of at least about 1 wt. %, at least about 5 wt. %, at least about 10 wt. %, at least about 20 wt. %, or at least about 30 wt. %, based on the total weight of the cell culture.

The facility can further comprise any structure capable of manufacturing the fuel component or fuel additive from the C₁₅ isoprenoid, such as α-farnesene, β-farnesene, nerolidol or farnesol. The structure may comprise a reactor for dehydrating the nerolidol or farnesol to α-farnesene or β-farnesene. Any reactor that can be used to convert an alcohol into an alkene under conditions known to skilled artisans may be used herein. The reactor may comprise a dehydrating catalyst disclosed herein. In some embodiments, the structure further comprises a mixer, a container, and a mixture of the dehydrating products from the dehydrating step.

The biosynthetic process of making C₁₅ isoprenoid compounds are disclosed in U.S. Pat. No. 7,399,323; U.S. Application Number US 2008/0274523; and PCT Publication Numbers WO 2007/140339 and WO 2007/139924, which are incorporated herein by reference.

α-Farnesene

α-Farnesene, whose structure is

is found in various biological sources including, but not limited to, the Dufour's gland in ants and in the coating of apple and pear peels. Biochemically, α-farnesene is made from FPP by α-farnesene synthase. Some non-limiting examples of suitable nucleotide sequences that encode such an enzyme include (DQ309034; Pyrus communis cultivar d'Anjou) and (AY182241; Malus domestica). See Pechouus et al., Planta 219(1):84-94 (2004). β-Farnesene

β-Farnesene, whose structure is

is found in various biological sources including, but not limited to, aphids and essential oils such as peppermint oil. In some plants such as wild potato, β-farnesene is synthesized as a natural insect repellent. Biochemically, β-farnesene is made from FPP by β-farnesene synthase. Some non-limiting examples of suitable nucleotide sequences that encode such an enzyme include (AF024615; Mentha x piperita) and (AY835398; Artemisia annua). See Picaud et al., Phytochemistry 66(9): 961-967 (2005). Farnesol

Farnesol, whose structure is

is found in various biological sources including insects and essential oils from cintronella, neroli, cyclamen, lemon grass, tuberose, and rose. Biochemically, farnesol is made from FPP by a hydroxylase such as farnesol synthase. Some non-limiting examples of suitable nucleotide sequences that encode such an enzyme include (AF529266; Zea mays) and (YDR481c; Saccharomyces cerevisiae). See Song, L., Applied Biochemistry and Biotechnology 128:149-158 (2006). Nerolidol

Nerolidol, whose structure is

is also known as peruviol which is found in various biological sources including essential oils from neroli, ginger, jasmine, lavender, tea tree, and lemon grass. Biochemically, nerolidol is made from FPP by a hydroxylase such as nerolidol synthase. A non-limiting example of a suitable nucleotide sequence that encodes such an enzyme includes AF529266 from Zea mays (maize; gene tps1).

The farnesol and nerolidol disclosed herein may be converted into α-farnesene, β-farnesene or a combination thereof by dehydration with a dehydrating agent or an acid catalyst. Any dehydrating agent or an acid catalyst that can convert an alcohol into an alkene can be used herein. Some non-limiting examples of suitable dehydrating agents or acid catalysts include phosphoryl chloride, anhydrous zinc chloride, phosphoric acid and sulfuric acid.

General Procedures of Making Polyfarnesenes

The polymerization of a farnesene or the copolymerization of a farnesene with a vinyl comonomer can be performed over a wide temperature range. In certain embodiments, the polymerization temperature is from about −30° C. to about 280° C., from about 30° C. to about 180° C., or from about 60° C. to about 100° C. The partial pressures of the vinyl comonomers can range from about 15 psig (0.1 MPa) to about 50,000 psig (245 MPa), from about 15 psig (0.1 MPa) to about 25,000 psig (172.5 MPa), from about 15 psig (0.1 MPa) to about 10,000 psig (69 MPa), from about 15 psig (0.1 MPa) to about 5,000 psig (34.5 MPa) or from about 15 psig (0.1 MPa) to about 1,000 psig (6.9 MPa).

The concentration of the catalyst used for making the polyfarnesenes disclosed herein depends on many factors. In some embodiment, the concentration ranges from about 0.01 micromoles per liter to about 100 micromoles per liter. The polymerization time depends on the type of process, the catalyst concentration, and other factors. Generally, the polymerization time is within several minutes to several hours.

A non-limiting example of solution polymerization procedure for farnesene homopolymer is outlined below. A farnesene such as β-farnesene can be added to a solvent such as cyclohexane to form a solution in a reactor which may be optionally under a nitrogen or argon atmosphere. The solution can be dried over a drying agent such as molecular sieves. A catalyst disclosed herein such as organolithium reagent and/or a Lewis base can be added into the reactor, and then the reactor is heated to an elevated temperature until all or a substantial portion of farnesene is consumed. The farnesene homopolymer can then be precipitated from the reaction mixture and dried in a vacuum oven.

A non-limiting example of solution polymerization procedure for a farnesene interpolymer is outlined below. A farnesene such as β-farnesene can be added to a solvent such as cyclohexane to form a farnesene solution in a reactor optionally under a nitrogen or argon atmosphere. The farnesene solution can be dried over a drying agent such as molecular sieves. In a second reactor optionally under nitrogen or argon atmosphere, a solution of styrene in cyclohexane with 10% is similarly prepared and dried over a drying agent such as molecular sieves. The styrene is polymerized by a catalyst such as organolithium reagent at an elevated temperature until all or a substantial portion of styrene is consumed. Then, the farnesene solution is transferred to the second reactor. The reaction is allowed to react until all or a substantial portion of farnesene is consumed. Then a dichlorosilane coupling agent (e.g., dichlorodimethylsilane in 1,2-dichloroethane) is then added into the second reactor to form a polyfarnesene.

Modified Polyfarnesenes

The polyfarnesenes disclosed herein can be modified by incorporating in their polymeric structures at least one modifier having at least one functional group to form modified polyfarnesenes. Any functional group that can react with one or more of the reactive end groups of the condensation polymers disclosed herein can be used herein. In some embodiments, the functional group is or comprises hydroxy, carboxyl, amino, epoxy, glycidyl, anhydride or a combination thereof.

In certain embodiments, the modified polyfarnesene is prepared by reacting a polyfarnesene disclosed herein with at least one modifier in the presence of a grafting initiator or radiation or a combination thereof. Any radiation disclosed herein for cross-linking polyfarnesene can be used herein. Any free radical initiator disclosed herein for cross-linking polyfarnesenes can be used as the grafting initiator. In certain embodiments, the grafting initiator is a dialkyl peroxide, a diacyl peroxide, a peroxyester, a peroxyketone, azobisisobutyronitrile or a combination thereof. In other embodiments, the grafting initiator is benzoyl peroxide, dicumyl peroxide, dilauryl peroxide, tert-butyl peroxyacetate, azobisisobutyronitrile or a combination thereof.

Any compound having at least one double bond and at least one functional group disclosed herein can be used as a modifier to prepare the modified polyfarnesene. In some embodiments, the modifier has formula (XVI), (XVII), (XVIII), (XIX) or (XX):

wherein each of Q′ and Q⁶ is independently O, S, NR²³ or N-Q⁷; each of Q², Q³, Q⁴ and Q⁵ is independently halo, Q⁸, NR²⁴R²⁵, OR²⁶ or O-Q⁸; Q⁷ and Q⁸ respectively have the following formulae:

wherein k is an integer from 1 to about 10; and Q⁹ is OH, NH₂, NHR³⁰, carboxyl, epoxy or glycidyl; and

each of R⁹ to R¹⁰ is independently H, C₁₋₂₀ alkyl, C₁₋₂₀ alkenyl, C₁₋₂₀ alkynyl, cycloalkyl, aryl, aralkyl, alkaryl, OH, NH₂, carboxyl, epoxy or glycidyl, or R¹⁹ and R²² together form a —(CH₂)_(m)— group where m is an integer from 1 to about 6, and wherein each of the C₁₋₂₀ alkyl, C₁₋₂₀ alkenyl, C₁₋₂₀ alkynyl, cycloalkyl, aryl, aralkyl, alkaryl, epoxy, glycidyl and —(CH₂)_(m)— is optionally substituted.

In certain embodiments, the modifier has formula (XVI). Some non-limiting examples of the modifiers having formula (XVI) include maleimide, maleic anhydride, citraconic anhydride, itaconic anhydride and combinations thereof. In some embodiments, the modified polyfarnesene prepared from the modifier having formula (XVI) has formula (XXI):

wherein R⁹, R¹⁰ and Q¹ are as defined herein and

is a polyfarnesene having formula (A). In some embodiments, the modifier is bonded to one of formulae (I)-(VIII) of formula (A). In other embodiments, the modifier is bonded to one of R¹, R², R³ and R⁴ of formula (A).

In some embodiments, the modifier has formula (XVII). Some non-limiting examples of the modifiers having formula (XVII) include mesaconic acid, maleic acid, fumaric acid, malenyl chloride, monomethyl maleate, dimethyl maleate, glycidyl maleate, dipropyl maleate, diisobutyl maleate, dihexyl maleate, dibenzyl maleate, p-chlorophenyl methyl maleate, phenylethyl maleate, dicyclopentyl meleate and combinations thereof. In some embodiments, the modified polyfarnesene prepared from the modifier having formula (XVII) has formula (XXII):

wherein R¹¹, R¹², Q² and Q³ are as defined herein and

is a polyfarnesene having formula (A). In some embodiments, the modifier is bonded to one of formulae (I)-(VIII) of formula (A). In other embodiments, the modifier is bonded to one of R¹, R², R³ and R⁴ of formula (A).

In certain embodiments, the modifier has formula (XVIII). Some non-limiting examples of the modifiers having formula (XVIII) include methacrylic acid, acrylic acid, itaconic acid, 2-hydroxyethyl methacrylate, 2-hydroxypropyl methacrylate, 3-hydroxypropyl methacrylate, 3-hydroxybutyl methacrylate, 4-hydroxybutyl methacrylate, caprolactone adduct of 2-hydroxyethyl methacrylate, ethylene oxide adduct of 2-hydroxyethyl methacrylate, propylene oxide adduct of 2-hydroxyethyl methacrylate, 2-hydroxyethyl acrylate, 2-hydroxypropyl acrylate, 3-hydroxypropyl acrylate, 3-hydroxybutyl acrylate, 4-hydroxybutyl acrylate, caprolactone adduct of 2-hydroxyethyl acrylate, ethylene oxide adduct of 2-hydroxyethyl acrylate, propylene oxide adduct of 2-hydroxyethyl acrylate, 2-hydroxyethyl crotonate, 2-hydroxypropyl crotonate, 3-hydroxypropyl crotonate, 3-hydroxybutyl crotonate, 4-hydroxybutyl crotonate, 5-hydroxypentyl crotonate, 6-hydroxyhexyl crotonate, glycidyl methacrylate, glycidyl acrylate, glycidyl ethacrylate, 3,4-epoxycyclohexylmethyl methacrylate, 3,4-epoxycyclohexylmethyl acrylate and combinations thereof. In some embodiments, the modified polyfarnesene prepared from the modifier having formula (XVIII) has formula (XXIIIA), (XXIIIB) or a combination thereof:

wherein R¹³, R¹⁴, R¹⁵ and Q⁴ are as defined herein and

is a polyfarnesene having formula (A). In some embodiments, the modifier is bonded to one of formulae (I)-(VIII) of formula (A). In other embodiments, the modifier is bonded to one of R¹, R², R³ and R⁴ of formula (A).

In some embodiments, the modifier has formula (XIX). Some non-limiting examples of the modifiers having formula (XIX) include allyl alcohol, hydroxymethyl vinyl ether, hydroxyethyl vinyl ether, hydroxypropyl vinyl ether, hydroxybutyl vinyl ether, hydroxypentyl vinyl ether, hydroxyhexyl vinyl ether, hydroxyheptyl vinyl ether, hydroxycyclohexyl vinyl ether, allylglycidyl ether, p-glycidyloxy styrene, p-glycidyloxy-α-methyl styrene, p-(3,4-epoxycyclohexylmethyloxy) styrene, p-(3,4-epoxycyclohexylmethyloxy)-α-methyl styrene, glycidyl ethylene, 3,4-epoxycyclohexylmethylethylene, glycidylvinyl ether, 3,4-epoxycyclohexylmethyl vinyl ether, 3,4-epoxycyclohexylmethyl allyl ether and combinations thereof. In some embodiments, the modified polyfarnesene prepared from the modifier having formula (XIX) has formula (XXIVA), (XXIVB) or a combination thereof:

wherein R¹⁶, R¹⁷, R¹⁸ and Q⁵ are as defined herein and

is a polyfarnesene having formula (A). In some embodiments, the modifier is bonded to one of formulae (I)-(VIII) of formula (A). In other embodiments, the modifier is bonded to one of R¹, R², R³ and R⁴ of formula (A).

In certain embodiments, the modifier has formula (XX). Some non-limiting examples of the modifiers having formula (XX) include bicyclo[2,2,2]-oct-5-ene-2,3-dicarboxylic acid anhydride, bicyclo[2,2,1]hept-5-ene-2,3-dicarboxylic acid anhydride and combinations thereof. In some embodiments, the modified polyfarnesene prepared from the modifier having formula (XX) has formula (XXV):

wherein R¹⁹, R²⁰, R²¹, R²² and Q⁶ are as defined herein and

is a polyfarnesene having formula (A). In some embodiments, the modifier is bonded to one of formulae (I)-(VIII) of formula (A). In other embodiments, the modifier is bonded to one of R¹, R², R³ and R⁴ of formula (A).

In some embodiments, the reaction of the polyfarnesene with the modifier is carried out in the presence of the grafting initiator at a temperature from about 25° C. to about 300° C. In other embodiments, the reaction temperature is from about 25° C. to about 250° C., from about 25° C. to about 200° C., from about 25° C. to about 150° C., from about 50° C. to about 300° C., from about 50° C. to about 250° C., from about 50° C. to about 200° C., from about 50° C. to about 150° C., from about 50° C. to about 140° C., from about 50° C. to about 130° C., from about 50° C. to about 120° C., or from about 50° C. to about 110° C.

The amount of the functional group present in the modified polyfarnesene may vary, depending on the ratio of the polyfarnesene to the modifier by weight. In some embodiments, the ratio of the polyfarnesene to the modifier is from about 100,000:1 to about 100:10, from about 100,000:1 to about 100:5, from about 100,000:1 to about 100:4, from about 100,000:1 to about 100:3, from about 100,000:1 to about 100:2, from about 100,000:1 to about 100:1, from about 100,000:1 to about 100:0.5, from about 100,000:1 to about 100:0.25, from about 100,000:1 to about 100:0.2, or from about 100,000:1 to about 100:0.1 by weight.

In certain embodiments, the functional group is present in an amount of at least about 0.1 wt. %, at least about 0.2 wt. %, at least about 0.3 wt. %, at least about 0.4 wt. %, or at least about 0.5 wt. %, based on the total weight of the polyfarnesene. In other embodiments, the functional group is present in an amount of at most about 10 wt. %, at most about 5 wt. %, at most about 4 wt. %, at most about 3 wt. %, at most about 2 wt. %, at most about 1 wt. %, at most about 0.5 wt. %, at most about 0.25 wt. %, or at most about 0.1 wt. %, based on the total weight of the polyfarnesene.

The reaction between the polyfarnesene and the modifier can be carried out in a solvent or in molten state. In some embodiments, the reaction is carried out in a solvent according to the following general procedure. A polyfarnesene disclosed herein (about 250 parts by weight) and a modifier (from about 0.1 parts to about 25 parts by weight) are added to about 5000 ml of a solvent, such as chlorobenzene and xylene. The resulting mixture is then agitated at a temperature from about 25° C. to the boiling point of the solvent to form a solution of the reactants. A solution (about 750 ml) of a grafting initiator such as benzoyl peroxide or dicumyl peroxide (from about 0.1 parts to about 2.5 parts by weight) in the solvent is then added dropwise to the solution of the reactants over a period from about 1 hour to about 16 hours, followed by heating the reaction mixture at a temperature from about 30° C. to the boiling point of the solvent for a period from about 1 hour to about 16 hours. The modified polyfarnesene is obtained by pouring the reaction mixture into a cold solvent, such as acetone. The modified polyfarnesene is filtered off, washed and dried.

In certain embodiments, the reaction between the polyfarnesene and the modifier is carried out in molten state according to the following general procedure. A polyfarnesene disclosed herein (about 250 parts by weight), a modifier (from about 0.1 parts to about 25 parts by weight), a grafting initiator such as benzoyl peroxide or dicumyl peroxide (from about 0.1 parts to about 2.5 parts by weight) are mixed in a mixer. The resulting mixture is extruded in an extruder at a screw speed of about 50-200 rpm and a barrel temperature profile ranging from about 100° C. to about 300° C. The extrudate is quenched in water and pelletized to form the modified polyfarnesene in pellet form.

Graft Copolymers Comprising Modified Polyfarnesenes

Graft copolymers can be prepared by reacting the modified polyfarnesenes disclosed herein with the condensation polymers disclosed herein at a temperature from about 50° C. to about 400° C. In some embodiments, the reaction temperature is from about 50° C. to about 350° C., from about 50° C. to about 300° C., from about 50° C. to about 250° C., from about 100° C. to about 400° C., from about 100° C. to about 350° C., from about 100° C. to about 300° C., from about 100° C. to about 250° C., from about 100° C. to about 200° C., from about 150° C. to about 400° C., from about 150° C. to about 350° C., or from about 150° C. to about 300° C. The reaction can be catalyzed by an acidic or a basic catalyst.

The reaction between the modified polyfarnesene and the condensation polymer can be carried out in a solvent or in molten state. In some embodiments, the reaction is carried out in a solvent according to the following general procedure. A modified polyfarnesene disclosed herein (about 100 parts by weight) and a condensation polymer (from about 10 parts to about 1000 parts by weight) are added to a solvent, such as ketones, alcohols, ethers, dimethylformamide and dimethyl sulfoxide. The reaction mixture is heated at a temperature from about 50° C. to the boiling point of the solvent for a period from about 1 hour to about 24 hours. The graft copolymer is obtained by pouring the reaction mixture into water. The graft copolymer is filtered off, washed and dried.

In certain embodiments, the reaction between the modified polyfarnesene and the condensation polymer is carried out in molten state according to the following general procedure. A modified polyfarnesene disclosed herein (about 100 parts by weight) and a condensation polymer (from about 10 parts to about 1000 parts by weight) are mixed in a mixer. The resulting mixture is extruded in an extruder at a screw speed of about 50-200 rpm and a barrel temperature profile ranging from about 150° C. to about 400° C. The extrudate is quenched in water and pelletized to form the graft copolymer in pellet form.

In some embodiments, the condensation polymer is a polyester, a polycarbonate, a polyamide, a polyether, a phenol-formaldehyde resin, an urea-formaldehyde resin, a melamine-formaldehyde resin or a combination thereof. In other embodiments, the condensation polymer is a polyester, a polycarbonate, a polyamide or a combination thereof. In certain embodiments, the condensation polymer is a polyester such as a hydroxyl-terminated polyester, a carboxyl-terminated polyester or an epoxy-terminated polyester. In other embodiments, the polyester is a polyethylene terephthalate such as a hydroxyl-terminated polyethylene terephthalate, a carboxyl-terminated polyethylene terephthalate or an epoxy-terminated polyethylene terephthalate. In certain embodiments, the condensation polymer is a polycarbonate such as a hydroxyl-terminated polycarbonate or an epoxy-terminated polycarbonate. In some embodiments, the condensation polymer is a polyamide such as an amino-terminated polyamide, a carboxyl-terminated polyamide or an epoxy-terminated polyamide.

In certain embodiments, the condensation polymer contains at least a hydroxy end group. In other embodiments, the condensation polymer is a hydroxyl-terminated condensation polymer such as a hydroxyl-terminated polyester, a hydroxyl-terminated polycarbonate, a hydroxyl-terminated polyether, a hydroxyl-terminated phenol-formaldehyde resin, a hydroxyl-terminated urea-formaldehyde resin or a hydroxyl-terminated melamine-formaldehyde resin. Any hydroxyl-terminated condensation polymer which is commercially available or known in the art can be used herein.

In certain embodiments, the graft copolymer is prepared by reacting a hydroxyl-terminated condensation polymer disclosed herein with the modified polyfarnesene of formula (XXI) where Q¹ is O; or the modified polyfarnesene of formula (XXII) where at least one of Q² and Q³ is Q⁸, OR²⁶ or O-Q⁸ where Q⁹ of Q⁸ is carboxyl, epoxy or glycidyl; or the modified polyfarnesene of formula (XXIIIA) or (XXIIIB) where Q⁴ is Q⁸, OR²⁶ or O-Q⁸ where Q⁹ of Q⁸ is carboxyl, epoxy or glycidyl; or the modified polyfarnesene of formula (XXIVA) or (XXIVB) where Q⁵ is Q⁸ or O-Q⁸ where Q⁹ of Q⁸ is carboxyl, epoxy or glycidyl; or the modified polyfarnesene of formula (XXV) where Q⁶ is O. The reaction can be catalyzed by any acidic or basic catalyst known by skilled artisans for promoting esterification or transesterification reactions.

In some embodiments, the condensation polymer contains at least an amino end group. In other embodiments, the condensation polymer is an amino-terminated polyamide. Any amino-terminated condensation polymer which is commercially available or known in the art can be used herein.

In certain embodiments, the graft copolymer is prepared by reacting an amino-terminated condensation polymer disclosed herein with the modified polyfarnesene of formula (XXI) where Q¹ is O; or the modified polyfarnesene of formula (XXII) where at least one of Q² and Q³ is Q⁸, OH or O-Q⁸ where Q⁹ of Q⁸ is carboxyl, epoxy or glycidyl; or the modified polyfarnesene of formula (XXIIIA) or (XXIIIB) where Q⁴ is Q⁸ or O-Q⁸ where Q⁹ of Q⁸ is carboxyl, epoxy or glycidyl; or the modified polyfarnesene of formula (XXIVA) or (XXIVB) where Q⁵ is Q⁸ or O-Q⁸ where Q⁹ of Q⁸ is carboxyl, epoxy or glycidyl; or the modified polyfarnesene of formula (XXV) where Q⁶ is O. The reaction can be catalyzed by any acidic or basic catalyst known by skilled artisans for promoting amidation reactions.

In certain embodiments, the condensation polymer contains at least a carboxyl end group. In other embodiments, the condensation polymer is a carboxyl-terminated condensation polymer such as a carboxyl-terminated polyester or a carboxyl-terminated polyamide. Any carboxyl-terminated condensation polymer which is commercially available or known in the art can be used herein.

In certain embodiments, the graft copolymer is prepared by reacting a carboxyl-terminated condensation polymer disclosed herein with the modified polyfarnesene of formula (XXII) where at least one of Q² and Q³ is Q⁸ or O-Q⁸ where Q⁹ of Q⁸ is OH, epoxy or glycidyl; or the modified polyfarnesene of formula (XXIIIA) or (XXIIIB) where Q⁴ is Q⁸ or O-Q⁸ where Q⁹ of Q⁸ is OH, epoxy or glycidyl; or the modified polyfarnesene of formula (XXIVA) or (XXIVB) where Q⁵ is Q⁸ or O-Q⁸ where Q⁹ of Q⁸ is OH, epoxy or glycidyl. The reaction can be catalyzed by any acidic or basic catalyst known by skilled artisans for promoting esterification reactions or transesterification reactions or reactions between a carboxylic acid group and an epoxy group.

In certain embodiments, the condensation polymer contains at least an epoxy end group. In other embodiments, the condensation polymer is an epoxy-terminated condensation polymer such as an epoxy-terminated polyester, an epoxy-terminated polycarbonate, an epoxy-terminated polyamide, an epoxy-terminated polyether, an epoxy-terminated phenol-formaldehyde resin, an epoxy-terminated urea-formaldehyde resin or an epoxy-terminated melamine-formaldehyde resin. Any epoxy-terminated condensation polymer which is commercially available or known in the art can be used herein.

In certain embodiments, the graft copolymer is prepared by reacting an epoxy-terminated condensation polymer disclosed herein with the modified polyfarnesene of formula (XXII) where at least one of Q² and Q³ is Q⁸, NHR²⁵, OH or O-Q⁸ where Q⁹ of Q⁸ is OH, NH₂, NHR³⁰ or carboxyl; or the modified polyfarnesene of formula (XXIIIA) or (XXIIIB) where Q⁴ is Q⁸, NHR²⁵, OH or O-Q⁸ where Q⁹ of Q⁸ is OH, NH₂, NHR³⁰ or carboxyl; or the modified polyfarnesene of formula (XXIVA) or (XXIVB) where Q⁵ is Q⁸, NHR²⁵, OH or O-Q⁸ where Q⁹ of Q⁸ is OH, NH₂, NHR³⁰ or carboxyl, where each of R²⁴ and R²⁶ is H. The reaction can be catalyzed by any acidic or basic catalyst known by skilled artisans for promoting reactions between an epoxy group and a hydroxy, amino or carboxyl group.

A skilled artisan can recognize that a graft copolymer comprising a polyfarnesene and a condensation polymer can also be prepared by reacting a modified condensation polymer comprising one or more vinyl groups with a polyfarnesene disclosed herein in the presence of a free radical initiator or a grafting modifier disclosed herein. The reaction can be carried out in a solvent or molten state. The modified condensation polymer can be obtained commercially or prepared by copolymerizing a suitable modifier having a vinyl group with the required comonomers for the condensation polymer. In some embodiments, the modifier can be a diol or a dicarboxylic acid having a vinyl group for making a modifier polyester. In certain embodiments, the modifier can be a diamine or a dicarboxylic acid having a vinyl group for making a modifier polyamide. In some embodiments, the modifier can be a diol having a vinyl group for making a modifier polycarbonate. In certain embodiments, the modifier can be a diol having a vinyl group for making a modifier polyether. In some embodiments, the modifier can be a phenol compound having a vinyl group for making a modifier phenol-formaldehyde resin. In certain embodiments, the modifier can be a melamine compound having a vinyl group for making a modifier melamine-formaldehyde resin. In some embodiments, the modifier can be a urea compound having a vinyl group for making a modifier urea-formaldehyde resin. In certain embodiments, the vinyl group is optionally substituted. In some embodiments, the vinyl group is acrylate, methacrylate, —CH═CH₂, allyl or a combination thereof.

Graft Copolymer Compositions

The graft copolymers disclosed herein can be used to prepare useful compositions or graft copolymer compositions. In some embodiments, the graft copolymer compositions comprise the polyfarnesene and an additive. In other embodiments, the graft copolymer compositions comprise the polyfarnesene and a second polymer. In certain embodiments, the graft copolymer compositions comprise the graft copolymer, an additive and a second polymer. In certain embodiments, the graft copolymer compositions do not comprise an additive or a second polymer.

The second polymer can be a vinyl polymer or copolymer, a non-vinyl polymer or copolymer, or a combination thereof. Some non-limiting examples of vinyl polymers and copolymers are disclosed in Malcolm P. Stevens, “Polymer Chemistry, an Introduction,” Third Edition, Oxford University Press, pp. 17-21 and 167-279 (1999), which is incorporated herein by reference. Some non-limiting examples of suitable second polymer include a polyolefin, polyurethane, polyester, polyamide, styrenic polymer, phenolic resin, polyacrylate, polymethacrylate or a combination thereof.

In certain embodiments, the ratio of the graft copolymer to the second polymer is from about 1:99 to about 99:1, from about 1:50 to about 50:1, from about 1:25 to about 25:1 or from about 1:10 to about 10:1.

In some embodiments, the second polymer is a polyolefin (e.g., polyethylene, polypropylene, an ethylene/α-olefin interpolymer, a copolymer of ethylene and propylene, and a copolymer of ethylene and vinyl acetate (EVA)), polyurethane, polyester, polyamide, styrenic polymer (e.g., polystyrene, poly(acrylonitrile-butadiene-styrene), poly(styrene-butadiene-styrene) and the like), phenolic resin, polyacrylate, polymethacrylate or a combination thereof. In some embodiments, the second polymer is polyethylene, polypropylene, polystyrene, a copolymer of ethylene and vinyl acetate, poly(acrylonitrile-butadiene-styrene), poly(styrene-butadiene-styrene) or a combination thereof. The second polymer may be blended with the graft copolymer before it is added to the graft copolymer composition. In some embodiments, the second polymer is added directly to the graft copolymer composition without pre-blending with the graft copolymer.

The weight ratio of the graft copolymer to the second polymer, such as EVA, in the graft copolymer composition can be between about 1:99 and about 99:1, between about 1:50 and about 50:1, between about 1:25 and about 25:1, between about 1:10 and about 10:1, between about 1:9 and about 9:1, between about 1:8 and about 8:1, between about 1:7 and about 7:1, between about 1:6 and about 6:1, between about 1:5 and about 5:1, between about 1:4 and about 4:1, between about 1:3 and about 3:1, between about 1:2 and about 2:1, between about 3:7 and about 7:3 or between about 2:3 and about 3:2.

In some embodiments, the second polymer is a polyolefin. Any polyolefin that is partially or totally compatible with the graft copolymer may be used. Non-limiting examples of suitable polyolefins include polyethylenes; polypropylenes; polybutylenes (e.g., polybutene-1); polypentene-1; polyhexene-1; polyoctene-1; polydecene-1; poly-3-methylbutene-1; poly-4-methylpentene-1; polyisoprene; polybutadiene; poly-1,5-hexadiene; interpolymers derived from olefins; interpolymers derived from olefins and other polymers such as polyvinyl chloride, polystyrene, polyurethane, and the like; and mixtures thereof. In some embodiments, the polyolefin is a homopolymer such as polyethylene, polypropylene, polybutylene, polypentene-1, poly-3-methylbutene-1, poly-4-methylpentene-1, polyisoprene, polybutadiene, poly-1,5-hexadiene, polyhexene-1, polyoctene-1 and polydecene-1.

Some non-limiting examples of suitable polyethylenes include ultra low density polyethylene (ULDPE), linear low density polyethylene (LLDPE), low density polyethylene (LDPE), medium density polyethylene (MDPE), high density polyethylene (HDPE), high molecular weight high density polyethylene (HMW-HDPE), ultra high molecular weight polyethylene (UHMW-PE) and combinations thereof. Some non-limiting examples of polypropylenes include low density polypropylene (LDPP), high density polypropylene (HDPP), high-melt strength polypropylene (HMS-PP) and combination thereof. In some embodiments, the second polymer is or comprises high-melt-strength polypropylene (HMS-PP), low density polyethylene (LDPE) or a combination thereof.

Optionally, the compositions disclosed herein comprise at least another additive for the purposes of improving and/or controlling the processibility, appearance, physical, chemical, and/or mechanical properties of the graft copolymer compositions. In some embodiments, the compositions do not comprise an additive. Any plastics additive known to a person of ordinary skill in the art may be used in the compositions disclosed herein. Non-limiting examples of suitable additives include plasticizers, oils, waxes, antioxidants, UV stabilizers, colorants or pigments, fillers, flow aids, coupling agents, crosslinking agents, surfactants, solvents, and combinations thereof. In certain embodiments, the additive is plasticizer, such as a mineral oil, liquid polybutene or a combination thereof.

The total amount of the additives can range from about greater than 0 to about 80%, from about 0.001% to about 70%, from about 0.01% to about 60%, from about 0.1% to about 50%, from about 1% to about 40%, or from about 10% to about 50% of the total weight of the graft copolymer composition. The amount of each of the additives can range from about greater than 0 to about 25%, from about 0.001% to about 20%, from about 0.01% to about 15%, from about 0.1% to about 10%, from about 0.1% to about 5%, or from about 0.1% to about 2.5% of the total weight of the graft copolymer composition. Some polymer additives have been described in Zweifel Hans et al., “Plastics Additives Handbook,” Hanser Gardner Publications, Cincinnati, Ohio, 5th edition (2001), which is incorporated herein by reference in its entirety.

Optionally, the compositions disclosed herein can comprise a tackifier. Some non-limiting examples of tackifiers include a natural and modified resin; a glycerol or pentaerythritol ester of natural or modified rosin; a copolymer or terpolymer of natured terpene; a polyterpene resin or a hydrogenated polyterpene resin; a phenolic modified terpene resin or a hydrogenated derivative thereof; an aliphatic or cycloaliphatic hydrocarbon resin or a hydrogenated derivative thereof; an aromatic hydrocarbon resin or a hydrogenated derivative thereof; an aromatic modified aliphatic or cycloaliphatic hydrocarbon resin or a hydrogenated derivative thereof; or a combination thereof. In certain embodiments, the tackifier has a ring and ball (R&B) softening point equal to or greater than 60° C., 70° C., 75° C., 80° C., 85° C., 90° C. or 100° C., as measured in accordance with ASTM 28-67, which is incorporated herein by reference. In certain embodiments, the tackifier has a R&B softening point equal to or greater than 80° C., as measured in accordance with ASTM 28-67.

In certain embodiments, the amount of tackifier in the compositions disclosed herein is from about 0.1 wt. % to about 70 wt. %, from about 0.1 wt. % to about 60 wt. %, from about 1 wt. % to about 50 wt. %, or from about 0.1 wt. % to about 40 wt. % or from about 0.1 wt. % to about 30 wt. % or from about 0.1 wt. % to about 20 wt. %, or from about 0.1 wt. % to about 10 wt. %, based on the total weight of the composition. In other embodiments, the amount of tackifier in the compositions disclosed herein is from about 1 wt. % to about 70 wt. %, from about 5 wt. % to about 70 wt. %, from about 10 wt. % to about 70 wt. %, from about 15 wt. % to about 70 wt. %, from about 20 wt. % to about 70 wt. %, or from about 25 wt. % to about 70 wt. %, based on the total weight of the composition.

Optionally, the compositions disclosed herein can comprise a wax, such as a petroleum wax, a low molecular weight polyethylene or polypropylene, a synthetic wax, a polyolefin wax, a beeswax, a vegetable wax, a soy wax, a palm wax, a candle wax or an ethylene/α-olefin interpolymer having a melting point of greater than 25° C. In certain embodiments, the wax is a low molecular weight polyethylene or polypropylene having a number average molecular weight of about 400 to about 6,000 g/mole. The wax can be present from about 10% to about 50% or 20% to about 40% by weight of the total composition.

Optionally, the compositions disclosed herein can comprise a plasticizer. In general, a plasticizer is a chemical that can increase the flexibility and lower the glass transition temperature of polymers. Any plasticizer known to a person of ordinary skill in the art may be added to the graft copolymer compositions disclosed herein. Non-limiting examples of plasticizers include mineral oils, abietates, adipates, alkyl sulfonates, azelates, benzoates, chlorinated paraffins, citrates, epoxides, glycol ethers and their esters, glutarates, hydrocarbon oils, isobutyrates, oleates, pentaerythritol derivatives, phosphates, phthalates, esters, polybutenes, ricinoleates, sebacates, sulfonamides, tri- and pyromellitates, biphenyl derivatives, stearates, difuran diesters, fluorine-containing plasticizers, hydroxybenzoic acid esters, isocyanate adducts, multi-ring aromatic compounds, natural product derivatives, nitriles, siloxane-based plasticizers, tar-based products, thioesters and combinations thereof. Where used, the amount of the plasticizer in the graft copolymer composition can be from greater than 0 to about 15 wt. %, from about 0.5 wt. % to about 10 wt. %, or from about 1 wt. % to about 5 wt. % of the total weight of the graft copolymer composition. Some plasticizers have been described in George Wypych, “Handbook of Plasticizers,” ChemTec Publishing, Toronto-Scarborough, Ontario (2004), which is incorporated herein by reference.

In some embodiments, the compositions disclosed herein optionally comprise an antioxidant that can prevent the oxidation of polymer components and organic additives in the graft copolymer compositions. Any antioxidant known to a person of ordinary skill in the art may be added to the graft copolymer compositions disclosed herein. Non-limiting examples of suitable antioxidants include aromatic or hindered amines such as alkyl diphenylamines, phenyl-α-naphthylamine, alkyl or aralkyl substituted phenyl-α-naphthylamine, alkylated p-phenylene diamines, tetramethyl-diaminodiphenylamine and the like; phenols such as 2,6-di-t-butyl-4-methylphenol; 1,3,5-trimethyl-2,4,6-tris(3′,5′-di-t-butyl-4′-hydroxybenzyl)benzene; tetrakis[(methylene(3,5-di-t-butyl-4-hydroxyhydrocinnamate)]methane (e.g., IRGANOX™ 1010, from Ciba Geigy, N.Y.); acryloyl modified phenols; octadecyl-3,5-di-t-butyl-4-hydroxycinnamate (e.g., IRGANOX™ 1076, commercially available from Ciba Geigy); phosphites and phosphonites; hydroxylamines; benzofuranone derivatives; and combinations thereof. Where used, the amount of the antioxidant in the graft copolymer composition can be from about greater than 0 to about 5 wt. %, from about 0.0001 to about 2.5 wt. %, from about 0.001 wt. % to about 1 wt. %, or from about 0.001 wt. % to about 0.5 wt. % of the total weight of the graft copolymer composition. Some antioxidants have been described in Zweifel Hans et al., “Plastics Additives Handbook,” Hanser Gardner Publications, Cincinnati, Ohio, 5th edition, Chapter 1, pages 1-140 (2001), which is incorporated herein by reference.

In other embodiments, the compositions disclosed herein optionally comprise an UV stabilizer that may prevent or reduce the degradation of the graft copolymer compositions by UV radiations. Any UV stabilizer known to a person of ordinary skill in the art may be added to the graft copolymer compositions disclosed herein. Non-limiting examples of suitable UV stabilizers include benzophenones, benzotriazoles, aryl esters, oxanilides, acrylic esters, formamidines, carbon black, hindered amines, nickel quenchers, hindered amines, phenolic antioxidants, metallic salts, zinc compounds and combinations thereof. Where used, the amount of the UV stabilizer in the graft copolymer composition can be from about greater than 0 to about 5 wt. %, from about 0.01 wt. % to about 3 wt. %, from about 0.1 wt. % to about 2 wt. %, or from about 0.1 wt. % to about 1 wt. % of the total weight of the graft copolymer composition. Some UV stabilizers have been described in Zweifel Hans et al., “Plastics Additives Handbook,” Hanser Gardner Publications, Cincinnati, Ohio, 5th edition, Chapter 2, pages 141-426 (2001), which is incorporated herein by reference.

In further embodiments, the compositions disclosed herein optionally comprise a colorant or pigment that can change the look of the graft copolymer compositions to human eyes. Any colorant or pigment known to a person of ordinary skill in the art may be added to the graft copolymer compositions disclosed herein. Non-limiting examples of suitable colorants or pigments include inorganic pigments such as metal oxides such as iron oxide, zinc oxide, and titanium dioxide, mixed metal oxides, carbon black, organic pigments such as anthraquinones, anthanthrones, azo and monoazo compounds, arylamides, benzimidazolones, BONA lakes, diketopyrrolo-pyrroles, dioxazines, disazo compounds, diarylide compounds, flavanthrones, indanthrones, isoindolinones, isoindolines, metal complexes, monoazo salts, naphthols, b-naphthols, naphthol AS, naphthol lakes, perylenes, perinones, phthalocyanines, pyranthrones, quinacridones, and quinophthalones, and combinations thereof. Where used, the amount of the colorant or pigment in the graft copolymer composition can be from about greater than 0 to about 10 wt. %, from about 0.1 wt. % to about 5 wt. %, or from about 0.25 wt. % to about 2 wt. % of the total weight of the graft copolymer composition. Some colorants have been described in Zweifel Hans et al., “Plastics Additives Handbook,” Hanser Gardner Publications, Cincinnati, Ohio, 5th edition, Chapter 15, pages 813-882 (2001), which is incorporated herein by reference.

Optionally, the compositions disclosed herein can comprise a filler which can be used to adjust, inter alia, volume, weight, costs, and/or technical performance. Any filler known to a person of ordinary skill in the art may be added to the graft copolymer compositions disclosed herein. Non-limiting examples of suitable fillers include talc, calcium carbonate, chalk, calcium sulfate, clay, kaolin, silica, glass, fumed silica, mica, wollastonite, feldspar, aluminum silicate, calcium silicate, alumina, hydrated alumina such as alumina trihydrate, glass microsphere, ceramic microsphere, thermoplastic microsphere, barite, wood flour, glass fibers, carbon fibers, marble dust, cement dust, magnesium oxide, magnesium hydroxide, antimony oxide, zinc oxide, barium sulfate, titanium dioxide, titanates and combinations thereof. In some embodiments, the filler is barium sulfate, talc, calcium carbonate, silica, glass, glass fiber, alumina, titanium dioxide, or a mixture thereof. In other embodiments, the filler is talc, calcium carbonate, barium sulfate, glass fiber or a mixture thereof. Where used, the amount of the filler in the graft copolymer composition can be from about greater than 0 to about 80 wt. %, from about 0.1 wt. % to about 60 wt. %, from about 0.5 wt. % to about 40 wt. %, from about 1 wt. % to about 30 wt. %, or from about 10 wt. % to about 40 wt. % of the total weight of the graft copolymer composition. Some fillers have been disclosed in U.S. Pat. No. 6,103,803 and Zweifel Hans et al., “Plastics Additives Handbook,” Hanser Gardner Publications, Cincinnati, Ohio, 5th edition, Chapter 17, pages 901-948 (2001), both of which are incorporated herein by reference.

Optionally, the graft copolymer compositions disclosed herein may be crosslinked, partially or completely. When crosslinking is desired, the graft copolymer compositions disclosed herein comprise a cross-linking agent that can be used to effect the cross-linking of the graft copolymer compositions, thereby increasing their modulus and stiffness, among other things. An advantage of a graft copolymer composition is that crosslinking can occur in its side chains instead of the polymer backbone like other polymers such as polyisoprene and polybutadiene. Any cross-linking agent known to a person of ordinary skill in the art may be added to the graft copolymer compositions disclosed herein. Non-limiting examples of suitable cross-linking agents include organic peroxides (e.g., alkyl peroxides, aryl peroxides, peroxyesters, peroxycarbonates, diacylperoxides, peroxyketals, and cyclic peroxides) and silanes (e.g., vinyltrimethoxysilane, vinyltriethoxysilane, vinyltris(2-methoxyethoxy)silane, vinyltriacetoxysilane, vinylmethyldimethoxysilane, and 3-methacryloyloxypropyltrimethoxysilane). Where used, the amount of the cross-linking agent in the polymer composition can be from about greater than 0 to about 20 wt. %, from about 0.1 wt. % to about 15 wt. %, or from about 1 wt. % to about 10 wt. % of the total weight of the polymer composition. Some suitable cross-linking agents have been disclosed in Zweifel Hans et al., “Plastics Additives Handbook,” Hanser Gardner Publications, Cincinnati, Ohio, 5th edition, Chapter 14, pages 725-812 (2001), both of which are incorporated herein by reference.

The cross-linking of the polyfarnesenes, modified polyfarnesenes, graft copolymers or the graft copolymer compositions disclosed herein can also be initiated by any radiation means known in the art, including, but not limited to, electron-beam irradiation, beta irradiation, gamma irradiation, corona irradiation, and UV radiation with or without cross-linking catalyst. U.S. patent application Ser. No. 10/086,057 (published as US2002/0132923 A1) and U.S. Pat. No. 6,803,014 disclose electron-beam irradiation methods that can be used in embodiments of the invention.

Irradiation may be accomplished by the use of high energy, ionizing electrons, ultra violet rays, X-rays, gamma rays, beta particles and the like and combination thereof. Preferably, electrons are employed up to 70 megarads dosages. The irradiation source can be any electron beam generator operating in a range of about 150 kilovolts to about 6 megavolts with a power output capable of supplying the desired dosage. The voltage can be adjusted to appropriate levels which may be, for example, 100,000, 300,000, 1,000,000 or 2,000,000 or 3,000,000 or 6,000,000 or higher or lower. Many other apparatuses for irradiating polymeric materials are known in the art. The irradiation is usually carried out at a dosage between about 3 megarads to about 35 megarads, preferably between about 8 to about 20 megarads. Further, the irradiation can be carried out conveniently at room temperature, although higher and lower temperatures, for example, 0° C. to about 60° C., may also be employed. Preferably, the irradiation is carried out after shaping or fabrication of the article. Also, in a preferred embodiment, the graft copolymer which has been incorporated with a pro-rad additive is irradiated with electron beam radiation at about 8 to about 20 megarads.

The cross-linking of the polyfarnesenes, modified polyfarnesenes, graft copolymers or the graft copolymer compositions disclosed herein can also be promoted with a crosslinking catalyst, and any catalyst that will provide this function can be used. Suitable catalysts generally include organic bases; carboxylic acids; organometallic compounds including organic titanates and complexes or carboxylates of lead, cobalt, iron, nickel, zinc and tin; dibutyltindilaurate, dioctyltinmaleate, dibutyltindiacetate, dibutyltindioctoate, stannous acetate, stannous octoate, lead naphthenate, zinc caprylate, cobalt naphthenate; and the like. The catalyst (or mixture of catalysts) is present in a catalytic amount, typically between about 0.015 and about 0.035 phr.

Blending of the Ingredients of the Graft Copolymer Compositions

The ingredients (i.e., the graft copolymer, the optional second polymer and additives) of the graft copolymer compositions disclosed herein, can be mixed or blended using methods known to a person of ordinary skill in the art. Non-limiting examples of suitable blending methods include melt blending, solvent blending, extruding, and the like.

In some embodiments, the ingredients of the compositions disclosed herein are melt blended by a method as described by Guerin et al. in U.S. Pat. No. 4,152,189. First, all solvents, if there are any, are removed from the ingredients by heating to an appropriate elevated temperature of about 100° C. to about 200° C. or about 150° C. to about 175° C. at a pressure of about 5 torr (667 Pa) to about 10 torr (1333 Pa). Next, the ingredients are weighed into a vessel in the desired proportions and the foam is formed by heating the contents of the vessel to a molten state while stirring.

In other embodiments, the ingredients of the compositions disclosed herein are processed using solvent blending. First, the ingredients are dissolved in a suitable solvent and the mixture is then mixed or blended. Next, the solvent is removed to provide the compositions disclosed herein.

In further embodiments, physical blending devices that can provide dispersive mixing, distributive mixing, or a combination of dispersive and distributive mixing can be used in preparing homogenous blends. Both batch and continuous methods of physical blending can be used. Non-limiting examples of batch methods include those methods using BRABENDER® mixing equipments (e.g., BRABENDER PREP CENTER®, available from C. W. Brabender Instruments, Inc., South Hackensack, N.J.) or BANBURY® internal mixing and roll milling (available from Farrel Company, Ansonia, Conn.) equipment. Non-limiting examples of continuous methods include single screw extruding, twin screw extruding, disk extruding, reciprocating single screw extruding, and pin barrel single screw extruding. In some embodiments, the additives can be added into an extruder through a feed hopper or feed throat during the extrusion of the graft copolymer, the optional second polymer or the foam. The mixing or blending of polymers by extrusion has been described in C. Rauwendaal, “Polymer Extrusion”, Hanser Publishers, New York, N.Y., pages 322-334 (1986), which is incorporated herein by reference.

When one or more additives are required in the compositions disclosed herein, the desired amounts of the additives can be added in one charge or multiple charges to the graft copolymer, the second polymer or the composition. Furthermore, the addition can take place in any order. In some embodiments, the additives are first added and mixed or blended with the graft copolymer and then the additive-containing graft copolymer is blended with the second polymer. In other embodiments, the additives are first added and mixed or blended with the second polymer and then the additive-containing second polymer is blended with the graft copolymer. In further embodiments, the graft copolymer is blended with the second polymer first and then the additives are blended with the composition.

The ingredients of the composition disclosed herein can be mixed or blended in any suitable mixing or blending devices known to skilled artisans. The ingredients in the composition disclosed herein can then be mixed at a temperature below the decomposition temperature of the ingredients to ensure that all ingredients are homogeneously mixed and remain intact.

Applications of the Compositions Comprising the Graft Copolymers

The graft copolymer compositions disclosed herein can be used as hot melt adhesives or pressure sensitive adhesives. It can be applied to manufacture any article that requires or comprises a hot melt adhesive or a pressure sensitive adhesive. Non-limiting examples of suitable articles include paper products, packaging materials, laminated wood panels, kitchen countertops, vehicles, labels, disposable diapers, hospital pads, feminine sanitary napkins, surgical drapes, tapes, cases, cartons, trays, medical devices, and bandages. In a further embodiment, the adhesive composition can be used in tapes, cases, cartons, trays, medical devices, and bandages.

In some embodiments, the compositions disclosed herein are used as hot melt adhesives. Such hot melt adhesive compositions can be used in industrial applications including packaging, particularly for low temperature use such as for dairy products or for freezer packaging of food products, and in sanitary disposable consumer articles, for example, diapers, feminine care pads, napkins, and the like. Some other suitable applications include book-binding, wood working and labeling. Some hot melt adhesives are described in A. V. Pocius, “Adhesion and Adhesives Technology,” Hanser Gardner Publications; 2nd edition, Chapter 10, pp. 270-280 (2002), and M. J Satriana, “Hot melt adhesives: Manufacture and applications,” Noyes Data Corp (1974), both of which are incorporated herein as reference.

In other embodiments, the compositions disclosed herein may be used as PSAs. Such PSA adhesive compositions can be applied to sheeting products (e.g., decorative, reflective, and graphical), labelstock, and tape backings. The substrate can be any suitable type of material depending on the desired application. In certain embodiments, the substrate comprises a nonwoven, paper, polymeric film (e.g., polypropylene (e.g., biaxially oriented polypropylene (BOPP)), polyethylene, polyurea, or polyester (e.g., polyethylene terephthalate (PET)), or release liner (e.g., siliconized liner). Some PSAs are described in A. V. Pocius, “Adhesion and Adhesives Technology,” Hanser Gardner Publications; 2nd edition, Chapter 9, pp. 238-259 (2002); and Istvan Benedek, “Technology of Pressure-Sensitive Adhesives and Products,” CRC; (2008), both of which are incorporated herein as reference.

In still other embodiments, the compositions can be utilized to form tape. For example, the PSA or hot melt adhesive composition is applied to at least one side of the backing of the tape. The adhesive composition may then be crosslinked to further improve its shear strength. Any suitable crosslinking method (e.g., exposure to radiation, such as ultraviolet or electron beam) or crosslinker additive (e.g., phenolic and silane curatives) may be utilized.

The adhesive compositions disclosed herein may be applied to the desired substrate or adhered in any manner known in the art, particularly those methods used traditionally for making tapes, cases, cartons, trays, medical devices, and bandages. In other embodiments, the adhesive compositions can be applied by a coating head or nozzle, with associated equipment. The adhesive compositions can be applied as fine lines, dots or spray coatings, in addition to other traditional forms as desired.

In some embodiments, the adhesive compositions can be applied using melt extrusion techniques. The adhesive composition can be applied by either continuous or batch processes. An example of a batch process is the placement of a portion of the adhesive composition between a substrate to which the adhesive composition is to be adhered and a surface capable of releasing the adhesive to form a composite structure. An example of a continuous forming method includes drawing the adhesive composition out of a heated film die and subsequently contacting the drawn composition to a moving plastic web or other suitable substrate.

In other embodiments, the adhesive compositions can be coated using a solvent-based method. For example, the solvent-based adhesive composition can be coated by such methods as knife coating, roll coating, gravure coating, rod coating, curtain coating, and air knife coating. The coated solvent-based adhesive composition is then dried to remove the solvent. Preferably, the applied solvent-based adhesive composition is subjected to elevated temperatures, such as those supplied by an oven, to expedite drying.

In certain embodiments, the compositions are used as hot-melt pressure-sensitive adhesives. Some hot-melt pressure-sensitive adhesives are described in Istvan Benedek, “Technology of Pressure-Sensitive Adhesives and Products,” CRC; Chapter 3, (2008), which is incorporated herein as reference.

In some embodiments, the compositions are used as rubber-based adhesives or contact bond adhesives. Some rubber-based adhesives or contact bond adhesives are described in A. V. Pocius, “Adhesion and Adhesives Technology,” Hanser Gardner Publications; 2nd edition, Chapter 9, pp. 259-265 (2002), which is incorporated herein as reference.

The following examples are presented to exemplify embodiments of the invention but are not intended to limit the invention to the specific embodiments set forth. Unless indicated to the contrary, all parts and percentages are by weight. All numerical values are approximate. When numerical ranges are given, it should be understood that embodiments outside the stated ranges may still fall within the scope of the invention. Specific details described in each example should not be construed as necessary features of the invention.

EXAMPLES

Purification of Starting Materials

β-farnesene having 97.6% purity by weight was obtained from Amyris Biotechnologies Inc., Emeryville, Calif. β-Farnesene included hydrocarbon-based impurities such as zingiberene, bisabolene, farnesene epoxide, farnesol isomer, E,E-farnesol, squalene, ergosterol, and some dimers of farnesene. β-farnesene was purified with a 3 Å molecular sieve to remove the impurities and were then redistilled under nitrogen atmosphere to improve purity. Cyclohexane was distilled under nitrogen atmosphere to eliminate moisture and stored with a drying agent.

Differential Scanning Calorimetry

A TA Q200 differential scanning calorimeter was utilized to determine glass transition temperatures (T_(g)) of polymer samples disclosed herein. A 5 mg sample was placed in an aluminum pan. An empty reference pan and the sample pan were maintained within ±0.01 mg. Samples were scanned from about −175° C. to about 75° C. at a rate of 10° C./min. T_(g) was identified as a step change transition in the heat flow. The mid-point of the transition was reported as the T_(g) of the sample.

Gel Permeation Chromatography

GPC was utilized to determine the molecular weights and polydispersities of polymer samples. A Waters 2414 refractive index detector was used with a Waters 1515 isocratic HPLC pump. HPLC grade tetrahydrofuran was used as solvent. Polydispersed fractions were collected from GPC. The molecular weight of a sample was generally recorded as the number averaged molecular weight (M_(n)) or the weight average (M_(w)). When there were overlapping peaks which prohibited the determination of a unique polydispersity of each peak, a peak molecular weight (M_(p)) was incorporated herein.

Thermal Gravimetric Analysis

The degradation temperatures of samples were determined by thermal gravimetric analysis (TGA). About 20 mg of a sample was placed in a tared pan. The pan was then loaded into a furnace. Air flow was allowed to equilibrate. The sample was then heated from room temperature to 580° C. at 10° C./min. Temperatures for 1% and 5% weight loss of samples were reported respectively.

Ultraviolet-Visible Spectroscopy

Ultraviolet-visible (UV-Vis) spectroscopy was utilized to monitor monomer consumption during the reaction. The reaction was allowed to continue until all monomers had been consumed. A Shimadzu UV-2450 UV-Vis spectrophotometer was utilized. Background measurement was averaged from five measurements with an empty quartz cuvette. Aliquots were periodically taken from the reaction vessel, which was then placed in a square quartz cuvette with having 1 cm beam distance. The absorbance of the sample is directly proportional to the concentration of the monomer in the aliquot. The progress of the reaction was monitored by UV-Vis spectroscopy with the characteristic absorption peak of β-farnesene at 230 nm.

Tensile Strength

Tensile strength of samples were determined using an INSTRON™ tensile tester. A sample was cast into films and cut to the appropriate dimensions. The thickness and width of the sample after processing were measured. A gauge length of 2.54 cm was used with a crosshead speed 25 mm/min.

Lap Test

Lap test was used to characterize adhesive properties of samples. Two substrates were held together by an adhesive. Substrates were then pulled apart, shearing the adhesive. The construct fails in one of three ways. When the substrate failed, it was called a substrate failure. When the adhesive was torn apart, it was called a cohesive failure. When the interface between the substrate and adhesive failed, it was called an adhesive failure. An INSTRON™ tensile tester was used to characterize the forces involved in the failure. The adhesive was applied to a 2 cm² section of the substrate with a crosshead speed of 25 mm/min. Aluminum was used as the substrate. Aluminum was cleaned with acetone before bonding.

¹H and ¹³C Nuclear Magnetic Resonance

¹H and ¹³C Nuclear Magnetic Resonance was utilized to characterize chemical microstructures of the samples. A Varian Mercury 300 MHz NMR was utilized for these measurements. Deuterated chloroform was used as the solvent. Several measurements were repeated for collecting spectra.

Example 1 1,4-Polyfarnesene Having a M_(n) of 105,000

To a dried three-neck reactor under argon atmosphere, a pre-dried solution comprising 92.29 g of β-farnesene in 13.7% in cyclohexane was added. n-Butyl lithium (1.85×10⁻³ mol, obtained from Acros, Morris Plains, N.J.) was added into the reactor as an initiator, and the reactor was heated at about 50° C. for about 19 hours, until all β-farnesene was consumed, monitored by UV-Vis spectroscopy. Example 1 was precipitated from the reaction mixture with a 1% solution of ethanol and t-butyl catachol (obtained from Sigma-Aldrich, St. Louis, Mo.). After drying in a vacuum oven at about 60° C. for about 2 hours, Example 1 was kept under vacuum for about 16 hours. Afterwards, Example 1, collected at 89.83 g (yield 97%), was stored in a refrigerator to prevent any crosslinking before characterization.

The progress of synthesizing Example 1 was monitored by the disappearance of β-farnesene, as measured by UV-Vis in the reaction mixture. FIG. 1 shows the Ultraviolet-Visible (UV-Vis) spectra of Example 1 and β-farnesene. The characteristic absorption peak of β-farnesene at 230 nm is present in the UV-Vis spectrum for β-farnesene in FIG. 1, but absent in the UV-Vis spectrum for Example 1 in FIG. 1.

The molecular weight and polydispersity of Example 1 were determined by GPC. FIG. 2 shows the GPC curve of Example 1. The number average molecular weight (M_(n)), weight average molecular weight (M_(w)), peak molecular weight (M_(p)), z average molecular weight (M_(z)), z+1 average molecular weight (M_(z+1)), M_(w)/M_(n), (i.e., polydispersity), M_(z)/M_(w), and M_(z+1)/M_(w) of Example 1 are shown in Table 1. The definitions of M_(n), M_(w), M_(z), M_(z+1), M_(p), and polydispersity can be found in Technical Bulletin TB021, “Molecular Weight Distribution and Definitions of MW Averages,” published by Polymer Laboratories, which is incorporated herein by reference. Some methods of measuring the molecular weights of polymers can be found in the book by Malcolm P. Stevens, “Polymer Chemistry: An Introduction,” Oxford University Press, Chapter 2 (1999), pp. 35-58, which is incorporated herein by reference. The number of farnesene units in Example 1 was calculated to be about 490.

TABLE 1 Properties Example 1 M_(n) 104,838 g/mol M_(w) 147,463 g/mol M_(p) 144,216 g/mol M_(z) 207,084 g/mol M_(z+1) 314,887 g/mol Polydispersity 1.406588 M_(z)/M_(w) 1.404311 M_(z+1)/M_(w) 2.135360

FIG. 3 shows the ¹³C NMR spectrum of Example 1. Peaks at 77.28 ppm, 77.02 ppm, and 76.77 ppm were peaks associated with the deuterated chloroform used for collecting the ¹³C NMR spectrum. The characteristic peak identifying Example 1 was at 139.05 ppm.

FIG. 4 shows the ¹H NMR spectrum of Example 1. Peaks at 4.85 ppm and 4.81 ppm were peaks associated with 3,4-microstructure. Peaks at 5.17 ppm, 5.16 ppm, 5.14 ppm, and 5.13 ppm were peaks associated with 1,4- and 3,4-microstructures. Based on the areas under the peaks of FIG. 4, about 12% of farnesene units in Example 1 was found to have 3,4-microstructure.

The DSC curve of Example 1 is shown in FIG. 5. The thermal characteristics of Example 1 were measured by DSC. The T_(g) of Example 1 was found to be about −76° C. No other thermal event was detected between −175° C. and 75° C.

The TGA curve of Example 1 measured in air is shown in FIG. 6. The decomposition temperature of Example 1 in air was determined by TGA. The 1% weight loss of Example 1 in air was recorded at 210° C. and the 5% weight loss of Example 1 in air was recorded at 307° C.

The TGA curve of Example 1 measured under nitrogen atmosphere is shown in FIG. 7. The 1% weight loss of Example 1 under nitrogen atmosphere was recorded at 307° C. and the 5% weight loss of Example 1 under nitrogen atmosphere was recorded at 339° C.

Example 1 was observed to be tacky. The lap test results of Example 1 are shown in FIG. 8. The adhesive capability of Example 1 was measured by the lap test. The adhesive energy of Example 1 was found to be about 11,400 J/m² with a peak stress of about 314 N/m².

Example 2 1,4-Polyfarnesene Having a M_(n) of 245,000

Example 2 is a 1,4-polyfarnesene having a M_(n) of about 245,000 g/mol. Example 2 was synthesized similarly according to the procedure for Example 1, except sec-butyl lithium was used as the initiator. The net weight of Example 2 was found to be 83.59 g (yield 71.4%). The yield is lower because aliquots were removed to monitor the progression of the reaction.

The molecular weight and polydispersity of Example 2 were determined by GPC. FIG. 9 shows the GPC curve of Example 2. The M_(n), M_(w), M_(p), M_(z), M_(Z+1), polydispersity, M_(z)/M_(w), and M_(z+1)/M_(w) of Example 2 are shown in Table 2. The number of farnesene units in Example 2 was calculated to be about 2000. Because of the increased molecular weight of Example 2, it had a higher level of entanglement and longer relaxation time than Example 1.

TABLE 2 Properties Example 2 M_(n) 244,747 g/mol M_(w) 457,340 g/mol M_(p) 501,220 g/mol M_(z) 768,187 g/mol M_(z+1) 1,132,362 g/mol   Polydispersity 1.868622 M_(z)/M_(w) 1.679684 M_(z+1)/M_(w) 2.475971

The DSC curve of Example 2 is shown in FIG. 10. The thermal characteristics of Example 2 were measured by DSC. The T_(g) of Example 2 was found to be about −76° C.

The tensile test results of Example 2 are shown in FIG. 11. The tensile strength of Example 2 was measured by a tensile test. Example 2 was observed to be soft, tacky and yielded quickly. As shown in FIG. 11, the peak elongation of Example 2 was found to be about 6% with a maximum tensile strength of about 19 psi. The modulus of Example 2 was calculated to be about 4.6 kpsi. Example 2 continued to yield to about 40% elongation.

Example 3 3,4-Polyfarnesene

Example 3 was synthesized similarly according to the procedure for Example 1 except that n-butyl lithium (1.71×10⁻³ mol) was added in the presence of N,N,N′,N′-tetramethylethylenediamine (1.71×10⁻³ mol, TMEDA, obtained from Sigma-Aldrich, St. Louis, Mo.). The net weight of Example 3 was found to be 82.72 g (yield 97%).

The molecular weight and polydispersity of Example 3 were determined by GPC. FIG. 12 shows the GPC curve of Example 3. The two peaks in FIG. 12 indicated that two distinct weight fractions formed in Example 3. The M_(n), M_(w), M_(z), M_(Z+1), polydispersity, M_(z)/M_(w), and M_(z+1)/M_(w) of Example 3 are shown in Table 3. The M_(p) of the first peak in FIG. 12 was about 97,165 g/mol. The M_(p) of the second peak in FIG. 12 was about 46,582 g/mol. The number of farnesene units in Example 3 was calculated to be about 240.

TABLE 3 Properties Example 3 M_(n) 45,818 g/mol M_(w) 47,644 g/mol M_(z) 49,134 g/mol M_(z+1) 50,527 g/mol Polydispersity 1.039844 M_(z)/M_(w) 1.031269 M_(z+1)/M_(w) 1.060509

FIG. 13 shows the ¹³C NMR spectrum of Example 3. Peaks at 77.33 ppm, 77.07 ppm, and 76.82 ppm were peaks of deuterated chloroform used for collecting the ¹³C NMR spectrum. The characteristic peak identifying Example 1 at 139.05 ppm was absent in FIG. 13, indicating a regular microstructure of Example 3.

FIG. 14 shows the ¹H NMR spectrum of Example 3. Peaks at 4.85 ppm and 4.81 ppm were peaks associated with 3,4-microstructure. Peaks at 5.21 ppm, 5.19 ppm, 5.18 ppm, 5.16 ppm, and 5.15 ppm were peaks associated with 1,4- and 3,4-microstructures. Based on the areas under the peaks of FIG. 14, about 10% of farnesene units in Example 3 was found to have 1,4-microstructure.

The DSC curve of Example 3 is shown in FIG. 15. The thermal characteristics of Example 3 were measured by DSC. The T_(g) of Example 3 was found to be about −76° C. No other thermal event was detected between −175° C. and 75° C.

The TGA curve of Example 1 measured in air is shown in FIG. 16. The decomposition temperature of Example 3 in air was determined by TGA. The 1% weight loss of Example 1 in air was recorded at 191° C. and the 5% weight loss of Example 1 in air was recorded at 265° C.

Example 3 was observed to be a highly tacky viscous fluid. The lap test results of Example 3 are shown in FIG. 17. The adhesive capability of Example 3 was measured by the lap test. The adhesive energy of Example 3 was found to be about 12,900 J/m² with a peak stress of about 430 N/m².

Example 4 Polystyrene-1,4-Polyfarnesene-Polystyrene

To a first dried three neck reactor under argon atmosphere, a pre-dried solution of 12% β-farnesene in cyclohexane was added. To a second dried three neck reactor under argon atmosphere, a 20.65 g solution of 10% styrene in cyclohexane was added. Afterwards, to the styrene solution, n-butyl lithium (6.88×10⁻⁴ mol) was added into the reactor as an initiator, and the reactor was heated at about 50° C. for about 16 hours, until all styrene was consumed, as monitored by GPC. Then, 161.8 β-farnesene solution (i.e., 19.61 g of β-farnesene) was transferred to the reactor under argon atmosphere. The reaction was allowed to react until completion for about 7 hours, monitored by GPC. Three equal aliquots of dichlorosilane coupling agent (3.44×10⁻⁴ mol, obtained from Acros, Morris Plains, N.J.) were then added into the reactor such that the mole ratio of Li to Cl of the reaction mixture was 1:2. The reaction mixture was allowed to react until completion as indicated by a color change from yellow to clear in the reactor. Example 4 was precipitated from the reaction mixture with a 1% solution of t-butyl catachol in ethanol. After drying in a vacuum oven at about 60° C. for about 2 hours, Example 4 was kept under vacuum for about 16 hours. Afterwards, Example 4, collected at 39.15 g (yield 97%), was stored in a refrigerator to prevent any crosslinking before characterization.

The GPC curve of polystyrene is shown in FIG. 18. The progress of polystyrene synthesis reaction was monitored by GPC. The two peaks in FIG. 18 indicated that there were two distinct weight fractions of polystyrene formed. The M_(n), M_(w), M_(z), M_(z+1), polydispersity, M_(z)/M_(w), and M_(z+1)/M_(w) of the polystyrene are shown in Table 4. The M_(p) of the first peak in FIG. 18 was found to be about 59,596 g/mol. The M_(p) of the second peak in FIG. 18 was found to be about 28,619 g/mol.

TABLE 4 Properties Polystyrene M_(n) 28,396 g/mol M_(w) 29,174 g/mol M_(z) 29,895 g/mol M_(z+1) 30,598 g/mol Polydispersity 1.027385 M_(z)/M_(w) 1.024739 M_(z+1)/M_(w) 1.048810

The polystyrene formed then acted as an initiator to initiate the polymerization with β-farnesene to form a polystyrene-1,4-polyfarnesene di-block copolymer. The GPC curve of the di-block copolymer is shown in FIG. 19. The progress of the di-block copolymer synthetic reaction was monitored by GPC. The three peaks in FIG. 19 indicated that there were three distinct weight fractions in the di-block copolymer reaction solution. The M_(n), M_(w), M_(p), M_(z), M_(z+1), polydispersity, M_(z)/M_(w), and M_(z+1)/M_(w) of the di-block copolymer are shown in Table 5. The M_(p) of the first peak in FIG. 19, corresponding to polystyrene-1,4-polyfarnesene-polystyrene, was found to be about 141,775 g/mol. The M_(p) of the second peak in FIG. 19, corresponding to the di-block copolymer, was found to be about 63,023 g/mol. The molecular weight of 1,4-polyfarnesene in the di-block copolymer was calculated to be about 35,000 g/mol. The M_(p) of the third peak in FIG. 19, corresponding to polystyrene, was found to be about 29,799 g/mol.

TABLE 5 Polystyrene-1,4-polyfarnesene Properties Di-block Copolymer M_(n) 29,434 g/mol M_(w) 30,345 g/mol M_(p) 29,799 g/mol M_(z) 31,172 g/mol M_(z+1) 31,936 g/mol Polydispersity 1.030949 M_(z)/M_(w) 1.027264 M_(z+1)/M_(w) 1.052449

The polystyrene-1,4-polyfarnesene di-block copolymer was further coupled to form Example 4. FIG. 20 shows the GPC curve of Example 4. The molecular weight and polydispersity of Example 4 were determined by GPC. The three peaks in FIG. 20 indicated that there were three distinct weight fractions for the coupling product formed. The M_(n), M_(w), M_(z), M_(z+1), polydispersity, M_(z)/M_(w), and M_(z+1)/M_(w) of the coupling product are shown in Table 6. The M_(p) of the first peak in FIG. 20, corresponding to Example 4, was found to be about 138,802 g/mol. Example 4 was obtained in about 10% of the coupling product. The number of farnesene monomer units in Example 4 was calculated to be about 300. The M_(p) of the second peak in FIG. 20, which corresponds to polystyrene-1,4-polyfarnesene di-block copolymers, was found to be about 63,691 g/mol. The M_(p) of the third peak in FIG. 20, corresponding to polystyrene, was found to be about 29,368 g/mol.

TABLE 6 Properties Example 4 M_(n) 138,240 g/mol M_(w) 142,147 g/mol M_(z) 146,636 g/mol M_(z+1) 151,848 g/mol Polydispersity 1.028264 M_(z)/M_(w) 1.031576 M_(z+1)/M_(w) 1.068242

FIG. 21 shows the ¹³C NMR spectrum of Example 4. Peaks at 77.68 ppm and 76.83 ppm were peaks of associated with the deuterated chloroform used for collecting the ¹³C NMR spectrum. Other peaks in FIG. 21 were peaks associated with 1,4-polyfarnesene and polystyrene. The characteristic peak identifying 1,4-polyfarnesene at 139.26 ppm was present in FIG. 21, indicating the presence of 1,4-polyfarnesene in Example 4.

FIG. 22 shows the ¹H NMR spectrum of Example 4. Peaks at 4.85 ppm and 4.81 ppm were peaks associated with 3,4-microstructure. Peaks at 5.10 ppm, 5.12 ppm, and 5.14 ppm were peaks associated with 1,4- and 3,4-microstructures. Based on the areas under the peaks of FIG. 22, about 3% of farnesene units in Example 4 was found to have 3,4-microstructure.

The DSC curve of Example 4 is shown in FIG. 23. The thermal characteristics of Example 4 were measured by DSC. The T_(g) of 1,4-polyfarnesene in Example 4 was found to be about −76° C. The T_(g) of polystyrene in Example 4 was found to be about 96° C. No other thermal event was detected between −175° C. and 75° C.

The TGA curve of Example 4 measured in air is shown in FIG. 24. The decomposition temperature of Example 4 in air was determined by TGA. The 1% weight loss of Example 4 in air was recorded at 307° C. and the 5% weight loss of Example 4 in air was recorded at 333° C.

The tensile test results of Example 4 are shown in FIG. 25. The tensile strength of Example 4 was measured by a tensile test. Example 4 was stiff but yielded. As shown in FIG. 25, the elongation at break of Example 4 was found to be about 425% with a maximum tensile strength of about 152 psi. The modulus of Example 4 was calculated to be about 31.9 kpsi. Stress at 330% elongation of Example 4 was about 122 psi.

Example 4 was observed to be tacky. The lap test results of Example 4, due to an adhesive failure, are shown in FIG. 26. The adhesive energy of Example 4 was found to be about 2,928,000 J/m² with a peak stress of about 134,000 N/m².

Example 5 Polystyrene-3,4-Polyfarnesene-Polystyrene

To a first dried three neck reactor under argon atmosphere, a pre-dried 12% solution of β-farnesene in cyclohexane was added. To a second dried three neck reactor under argon atmosphere, a pre-dried solution of 10% styrene in cyclohexane was added. Afterwards, 141.1 g of the styrene solution (i.e., 14.82 g of styrene) was transferred to a dried reactor under argon atmosphere. A mixture of n-butyl lithium (5.84×10⁻⁴ mol) and TMEDA (5.02×10⁻⁴ mol) was added into the reactor as an initiator, and the reactor was heated at about 50° C. for about 16 hours, until all styrene was consumed, as monitored by GPC. Then, 143.07 g of β-farnesene solution (i.e., 15.74 g of β-farnesene) was transferred to the reactor under argon atmosphere. The reaction was allowed to react until completion for about 16 hours, as monitored by GPC. Dichlorosilane coupling agent was then added into the reactor in three equal aliquots, such that the mole ratio of Li to Cl was 1:2. The reaction mixture was allowed react until completion as indicated by a color change from yellow to clear in the reactor. Example 5 was precipitated from the reaction mixture by a 1% solution of t-butyl catachol in ethanol. After drying in a vacuum oven at about 60° C. for about 2 hours, Example 5 was kept under vacuum for about 16 hours. Afterwards, Example 5, collected at 28.75 g (yield 96%), was stored in a refrigerator to prevent any crosslinking before characterization.

The GPC curve of polystyrene is shown in FIG. 27. The progress of synthesizing polystyrene was monitored by GPC. The two peaks in FIG. 27 indicated that there were two distinct weight fractions of polystyrene. The M_(n), M_(w), M_(z), M_(z+1), polydispersity, M_(z)/M_(w), and M_(z+1)/M_(w) of polystyrene are shown in Table 7. The M_(p) of the first peak in FIG. 27 was found to be about 65,570 g/mol. The M_(p) of the second peak in FIG. 27 was found to be about 32,122 g/mol.

TABLE 7 Properties Polystyrene M_(n) 27,915 g/mol M_(w) 30,898 g/mol M_(z) 32,608 g/mol M_(z+1) 33,819 g/mol Polydispersity 1.106849 M_(z)/M_(w) 1.055361 M_(z+1)/M_(w) 1.094557

The polystyrene formed then acted as an initiator to initiate the polymerization with β-farnesene to form a polystyrene-3,4-polyfarnesene di-block copolymer. The GPC curve of the di-block copolymer is shown in FIG. 28. The progress of the di-block copolymer synthesis was monitored by GPC. The three peaks in FIG. 28 indicated that there were three distinct weight fractions in the di-block copolymer reaction solution. The M_(n), M_(w), M_(z), M_(z+1), polydispersity, M_(z)/M_(w), and M_(z+1)/M_(w) of the di-block copolymer are shown in Table 8. The M_(p) of the first peak in FIG. 28, corresponding to polystyrene-3,4-polyfarnesene-polystyrene, was found to be about 174,052 g/mol. The M_(p) of the second peak in FIG. 28, corresponding to the di-block copolymer, was found to be about 86,636 g/mol. The molecular weight of 3,4-polyfarnesene in the di-block copolymer was calculated to be about 54,000 g/mol. The M_(p) of the third peak in FIG. 28, corresponding to polystyrene, was found to be about 33,955 g/mol.

TABLE 8 Polystyrene-3,4-polyfarnesene Properties Di-block Copolymer M_(n) 27,801 g/mol M_(w) 31,379 g/mol M_(z) 33,539 g/mol M_(z+1) 35,033 g/mol Polydispersity 1.128697 M_(z)/M_(w) 1.068833 M_(z+1)/M_(w) 1.116447

The polystyrene-3,4-polyfarnesene di-block copolymer was further coupled to form Example 5. FIG. 29 shows the GPC curve of Example 5. The molecular weight and polydispersity of Example 5 were determined by GPC. The three peaks in FIG. 29 indicated that there were three distinct weight fractions for the coupling product formed. The M_(n), M_(w), M_(z), M_(z+1), polydispersity, M_(z)/M_(w), and M_(z+1)/M_(w) of Example 5 are shown in Table 9. The M_(p) of the first peak in FIG. 29, corresponding to Example 5, was found to be about 148,931 g/mol. Example 5 was obtained at about 33% of the coupling product. The number of farnesene monomer units in Example 5 was calculated to be about 300. The peak molecular weight of the blocks in Example 5 was found to be about 32,000-108,000-32,000 g/mol. The M_(p) of the second peak in FIG. 29, corresponding to the polystyrene-3,4-polyfarnesene di-block copolymer, was found to be about 81,424 g/mol. The M_(p) of the third peak in FIG. 29, corresponding to polystyrene, was found to be about 32,819 g/mol.

TABLE 9 Properties Example 4 M_(n) 28,179 g/mol M_(w) 30,815 g/mol M_(z) 32,590 g/mol M_(z+1) 33,905 g/mol Polydispersity 1.093554 M_(z)/M_(w) 1.057606 M_(z+1)/M_(w) 1.100250

FIG. 30 shows the ¹³C NMR spectrum of Example 5. Peaks at 77.72 ppm, 77.29 ppm, and 76.87 ppm were peaks of associated with the deuterated chloroform used for collecting the ¹³C NMR spectrum. Other peaks in FIG. 30 were peaks associated with 3,4-polyfarnesene and polystyrene. The characteristic peak identifying 1,4-polyfarnesene at 139.05 ppm was absent in FIG. 30, indicating a regular microstructure of Example 5.

FIG. 31 shows the ¹H NMR spectrum of Example 5. Peaks at 4.85 ppm and 4.81 ppm were peaks associated with 3,4-microstructure. Peaks at 5.15 ppm and 5.13 ppm were peaks associated with 1,4- and 3,4-microstructures. Based on the areas under the peaks of FIG. 31, about 5% of farnesene units in Example 5 was found to have 1,4-microstructure.

The DSC curve of Example 5 is shown in FIG. 32. The thermal characteristics of Example 5 were measured by DSC. The T_(g) of 3,4-polyfarnesene in Example 5 was found to be about −72° C. The T_(g) of polystyrene in Example 5 was found to be about 94° C. No other thermal event was detected between −175° C. and 75° C.

The TGA curve of Example 5 measured in air is shown in FIG. 33. The decomposition temperature of Example 5 in air was determined by TGA. The 1% weight loss of Example 5 in air was recorded at 240° C. and the 5% weight loss of Example 5 in air was recorded at 327° C.

The tensile test results of Example 5 are shown in FIG. 34. The tensile strength of Example 5 was measured by a tensile test. Example 5 was stiff but yielded. As shown in FIG. 34, the elongation at break of Example 5 was found to be about 175% with a maximum tensile strength of about 768 psi. The modulus of Example 5 was calculated to be about 39.5 kpsi.

Example 5 was further purified by repeated extraction with solvent hexane 4 times. The GPC curve of the purified Example 5 is shown in FIG. 35. The extraction of Example 5 from the coupling product was evaluated by GPC. After the extraction, Example 5, shown as the first peak in FIG. 35, was increased to about 60% of the extracted product. The polystyrene-3,4-polyfarnesene di-block copolymer, shown as the second peak in FIG. 35, was reduced to about 30% of the extracted product. Polystyrene, shown as the third peak in FIG. 35, was reduced to about 10% of the extracted product.

The GPC curve of the extraction solvent hexane is shown in FIG. 36. After the extraction, Example 5 existed in very low amount in the extraction solvent, shown as the first peak in FIG. 36. A significant amount of the polystyrene-3,4-polyfarnesene di-block copolymer was extracted to the extraction solvent, shown as the second peak in FIG. 36. A majority of polystyrene was extracted to the extraction solvent, shown as the third peak in FIG. 36.

The tensile test results of the purified Example 5 are shown in FIG. 37. The tensile strength of the purified Example 5 was measured by a tensile test. Example 5 was soft and readily yielded. As shown in FIG. 37, the elongation at break of the purified Example 5 was found to be about 550% with a maximum tensile strength of about 340 psi. The modulus of the purified Example 5 was calculated to be about 65.9 kpsi. Stress at 300% elongation of the purified Example 5 was found to be about 133 psi.

Example 6 Maleic Anhydride Modified Polyfarnesene (Solvent)

Example 1 (about 250 parts by weight) and maleic anhydride (about 50 parts by weight) are added to about 5000 ml of a solvent, such as chlororbenzene. The resulting mixture is then agitated at 110° C. to form a solution of reactants. A solution (about 750 ml) of benzoyl peroxide (about 2.5 parts by weight) in the solvent is then added dropwise to the solution of reactants over 2 hours, followed by heating the reaction mixture at 110° C. for 3 hours. The product is obtained by pouring the reaction mixture into a cold solvent, such as acetone. The product (i.e., maleic anhydride modified polyfarnesene) is filtered off, washed and dried.

Example 7 2-Hydroxyethyl Methacrylate Modified Polyfarnesene (Solvent)

Example 1 (about 250 parts by weight) and 2-hydroxyethyl methacrylate (about 75 parts by weight) are added to about 5000 ml of a solvent, such as xylene, contained in a flask with an agitator under nitrogen atmosphere. The resulting mixture is then agitated at 110° C. to form a solution of reactants. A solution (about 500 ml) of benzoyl peroxide (about 2.5 parts by weight) in the solvent is then added dropwise to the solution of reactants over 2 hours, followed by heating the reaction mixture at 110° C. for 3 hours. The product is obtained by pouring the reaction mixture into a cold solvent, such as acetone. The product (i.e., 2-hydroxyethyl methacrylate modified polyfarnesene) is filtered off, washed and then dried.

Example 8 Glycidyl Methacrylate Modified Polyfarnesene (Solvent)

Example 1 (about 250 parts by weight) and glycidyl methacrylate (about 75 parts by weight) are added to about 5000 ml of a solvent, such as xylene, contained in a flask with an agitator under nitrogen atmosphere. The resulting mixture is then agitated at 110° C. to form a solution of reactants. A solution (about 500 ml) of benzoyl peroxide (about 2.5 parts by weight) in the solvent is then added dropwise to the solution of reactants over 2 hours, followed by heating the reaction mixture at 110° C. for 3 hours. The product is obtained by pouring the reaction mixture into a cold solvent, such as acetone. The product (i.e., glycidyl methacrylate modified polyfarnesene) is filtered off, washed and then dried.

Example 9 Maleic Anhydride Modified Polyfarnesene (Extruder)

Example 4 (about 100 parts by weight), maleic anyhydride (about 1.5 parts by weight), dicumyl peroxide (about 0.1 parts by weight) are mixed in a mixer. The resulting mixture is extruded in an extruder at a screw speed of about 50-200 rpm and a barrel temperature profile ranging from about 100° C. to about 300° C., quenched in water and pelletized to form the maleic anhydride modified polyfarnesene in pellet form.

Example 10 1-(4-Hydroxyphenyl)Succinimide Modified Polyfarnesene (Extruder)

Example 9 (about 100 parts by weight) is mixed in a mixer with m-aminophenol (about 1.7 parts by weight). The resulting mixture is extruded in an extruder at a screw speed of 25-200 rpm and a barrel temperature profile ranging from about 100° C. to about 300° C., quenched in water and pelletized to form the 1-(4-hydroxyphenyl)succinimide modified polyfarnesene in pellet form.

Example 11 Glycidyl Methacrylate Modified Polyfarnesene (Extruder)

Example 4 (about 100 parts by weight), glycidyl methacrylate (about 1.5 parts by weight), dicumyl peroxide (about 0.1 parts by weight) are mixed in a mixer. The resulting mixture is extruded in an extruder at a screw speed of about 50-200 rpm and a barrel temperature profile ranging from about 100° C. to about 300° C., quenched in water and pelletized to form the glycidyl methacrylate modified polyfarnesene in pellet form.

Example 12 Maleic Anhydride Modified Polyfarnesene-g-Polyester

A maleic anhydride modified polyfarnesene-g-polyester is produced by melt blending Example 6 or Example 9 with a hydroxyl-terminated polyester at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 13 Maleic Anhydride Modified Polyfarnesene-g-Polycarbonate

A maleic anhydride modified polyfarnesene-g-polycarbonate is produced by melt blending Example 6 or Example 9 with a hydroxyl-terminated polycarbonate at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 14 Maleic Anhydride Modified Polyfarnesene-g-Polyamide

A maleic anhydride modified polyfarnesene-g-polyamide is produced by melt blending Example 6 or Example 9 with an amino-terminated polyamide at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 15 Maleic Anhydride Modified Polyfarnesene-g-Phenobic Novolak Resin

A maleic anhydride modified polyfarnesene-g-phenobic novolak resin is produced by melt blending Example 6 or Example 9 with phenobic novolak resin at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 16 2-Hydroxyethyl Methacrylate Modified Polyfarnesene-g-Polyester

A 2-hydroxyethyl methacrylate modified polyfarnesene-g-polyester is produced by melt blending Example 7 with a carboxyl-terminated or epoxy-terminated polyester at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 17 1-(4-Hydroxyphenyl)Succinimide Modified Polyfarnesene-g-Polyester

A 1-(4-hydroxyphenyl)succinimide modified polyfarnesene-g-polyester is produced by melt blending Example 10 with a carboxyl-terminated or epoxy-terminated polyester at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 18 2-Hydroxyethyl Methacrylate Modified Polyfarnesene-g-Polyamide

A 2-hydroxyethyl methacrylate modified polyfarnesene-g-polyamide is produced by melt blending Example 7 with a carboxyl-terminated or epoxy-terminated polyamide at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 19 1-(4-Hydroxyphenyl)Succinimide Modified Polyfarnesene-g-Polyamide

A 1-(4-hydroxyphenyl)succinimide modified polyfarnesene-g-polyamide is produced by melt blending Example 10 with a carboxyl-terminated or epoxy-terminated polyamide at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 20 Glycidyl Methacrylate Modified Polyfarnesene-g-Polyester

A glycidyl methacrylate modified polyfarnesene-g-polyester is produced by melt blending Example 8 or Example 11 with a hydroxyl-terminated or carboxyl-terminated polyester at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 21 Glycidyl Methacrylate Modified Polyfarnesene-g-Polycarbonate

A glycidyl methacrylate modified polyfarnesene-g-polycarbonate is produced by melt blending Example 8 or Example 11 with a hydroxyl-terminated or carboxyl-terminated polycarbonate at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 22 Glycidyl Methacrylate Modified Polyfarnesene-g-Polyamide

A glycidyl methacrylate modified polyfarnesene-g-polyamide is produced by melt blending Example 8 or Example 11 with a amino-terminated or carboxyl-terminated polyamide at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

Example 23 Glycidyl Methacrylate Modified Polyfarnesene-g-Phenobic Novolak Resin

A glycidyl methacrylate modified polyfarnesene-g-phenobic novolak resin is produced by melt blending Example 8 or Example 11 with a phenobic novolak resin at about 200° C. to about 400° C. in the extruder. The resulting melt blend is extruded and quenched in water and pelletized to yield the product in pellet form.

While the invention has been described with respect to a limited number of embodiments, the specific features of one embodiment should not be attributed to other embodiments of the invention. No single embodiment is representative of all aspects of the invention. In some embodiments, the compositions or methods may include numerous compounds or steps not mentioned herein. In other embodiments, the compositions or methods do not include, or are substantially free of, any compounds or steps not enumerated herein. Variations and modifications from the described embodiments exist. Finally, any number disclosed herein should be construed to mean approximate, regardless of whether the word “about” or “approximately” is used in describing the number. The appended claims intend to cover all those modifications and variations as falling within the scope of the invention. 

What is claimed is:
 1. A graft copolymer of a polyfarnesene with a condensation polymer, wherein the condensation polymer is a polyester, a polycarbonate, a polyamide, a polyether, a phenol-formaldehyde resin, an urea-formaldehyde resin, a melamine-formaldehyde resin or a combination thereof.
 2. The graft copolymer of claim 1, wherein the condensation polymer is a polyester, a polycarbonate, a polyamide or a combination thereof.
 3. The graft copolymer of claim 1, wherein the condensation polymer is a polyester.
 4. The graft copolymer of claim 3, wherein the polyester is a polyethylene terephthalate.
 5. The graft copolymer of claim 1, wherein the polyfarnesene has formula (A):

wherein m is from 0 to about 100,000; n is from 1 to about 100,000 with the proviso that when m is 0, n is from 2 to about 100,000; X has one or more of formulae (I)-(VIII):

Y has formula (IX):

wherein R¹ has formula (XI):

R² has formula (XII):

R³ has formula (XIII):

and R⁴ has formula (XIV):

wherein each of R⁵, R⁶, R⁷ and R⁸ is independently H, alkyl, cycloalkyl, aryl, cycloalkenyl, alkynyl, heterocyclyl, alkoxy, aryloxy, carboxy, alkoxycarbonyl, aminocarbonyl, alkylaminocarbonyl, dialkylaminocarbonyl, acyloxy, nitrile or halo.
 6. The graft copolymer of claim 5, wherein the amount of formula (I) is at most about 80 wt. % and the amount of formula (II) is from about 5 wt. % to about 99 wt. %, based on the total weight of the polyfarnesene.
 7. The graft copolymer of claim 5, wherein the mole percent ratio of X to Y is from about 1:4 to about 100:1 when m is 1 or greater.
 8. The graft copolymer of claim 5, wherein m is 0 and n is from 2 to about 100,000.
 9. The graft copolymer of any of claim 5, wherein m is from 1 to about 100,000 and n is from 1 to about 100,000, and wherein the polyfarnesene is a random farnesene interpolymer.
 10. The graft copolymer of claim 5, wherein m is from 1 to about 100,000 and n is from 1 to about 100,000, and wherein the polyfarnesene is a block farnesene interpolymer.
 11. The graft copolymer of claim 1, wherein the polyfarnesene is prepared by polymerizing β-farnesene or α-farnesene or a combination thereof in the presence of a catalyst.
 12. The graft copolymer of claim 11, wherein the β-farnesene or α-farnesene is copolymerized with a vinyl monomer to form a farnesene interpolymer.
 13. A modified polyfarnesene prepared by reacting a polyfarnesene with at least one modifier in the presence of a grafting initiator, radiation or a combination thereof, wherein the ratio of the polyfarnesene to the modifier is from about 100,000:1 to about 100:5 by weight, and wherein the modifier has formula (XVI), (XVII), (XVIII), (XIX), or (XX):

wherein Q¹ is S, NR²³ or N-Q⁷; Q⁶ is O, S, NR²³ or N-Q⁷; each of Q², Q³ and Q⁴ is independently halo, Q⁸, or NR²⁴R²⁵, Q⁵ is halo, Q⁸, NR²⁴R²⁵, OR²⁶ or O-Q⁸; Q⁷ and Q⁸ respectively have the following formulae:

wherein k is an integer from 1 to about 10; and Q⁹ is OH, NH₂, NHR³⁰, carboxyl, epoxy or gycidyl; and each of R⁹ to R³⁰is independently H, C₁₋₂₀ alkyl, C₁₋₂₀ alkenyl, C₁₋₂₀ alkynyl, cycloalkyl, aryl, aralkyl, alkaryl, OH, NH₂, carboxyl, epoxy or gycidyl, or R¹⁹ and R²² together form a —(CH₂)_(m)— group where m is an integer from 1 to about 6, and wherein each of the C₁-₂₀ alkyl, C₁₋₂₀ alkenyl, C₁₋₂₀ alkynyl, cycloalkyl, aryl, aralkyl, alkaryl, epoxy, gycidyl and —(CH₂)_(m)— is optionally substituted.
 14. The modified polyfarnesene of claim 13, wherein the modifier has formula (XVI).
 15. The modified polyfarnesene of claim 14, wherein the modifier is maleimide, citraconic anhydride, itaconic anhydride or a combination thereof.
 16. The modified polyfarnesene of claim 13, wherein the modifier has formula (XVII).
 17. The modified polyfarnesene of claim 16, wherein the modifier is mesaconic acid, maleic acid, fumaric acid, malenyl chloride, monomethyl maleate, dimethyl maleate, glycidyl maleate, dipropyl maleate, diisobutyl maleate, dihexyl maleate, dibenzyl maleate, p-chlorophenyl methyl maleate, phenylethyl maleate, dicyclopentyl meleate or a combination thereof
 18. The modified polyfarnesene of claim 13, wherein the modifier has formula (XVIII).
 19. The modified polyfarnesene of claim 18, wherein the modifier is methacrylic acid, acrylic acid, itaconic acid, 2-hydroxyethyl methacrylate, 2-hydroxypropyl methacrylate, 3-hydroxypropyl methacrylate, 3-hydroxybutyl methacrylate, 4-hydroxybutyl methacrylate, caprolactone adduct of 2-hydroxyethyl methacrylate, ethylene oxide adduct of 2-hydroxyethyl methacrylate, propylene oxide adduct of 2-hydroxyethyl methacrylate, 2-hydroxyethyl acrylate, 2-hydroxypropyl acrylate, 3-hydroxypropyl acrylate, 3-hydroxybutyl acrylate, 4-hydroxybutyl acrylate, caprolactone adduct of 2-hydroxyethyl acrylate, ethylene oxide adduct of 2-hydroxyethyl acrylate, propylene oxide adduct of 2-hydroxyethyl acrylate, 2-hydroxyethyl crotonate, 2-hydroxypropyl crotonate, 3-hydroxypropyl crotonate, 3-hydroxybutyl crotonate, 4-hydroxybutyl crotonate, 5-hydroxypentyl crotonate, 6-hydroxyhexyl crotonate, glycidyl methacrylate, glycidyl acrylate, glycidyl ethacrylate, 3,4-epoxycyclohexylmethyl methacrylate, 3,4-epoxycyclohexylmethyl acrylate or a combination thereof.
 20. The modified polyfarnesene of claim 13, wherein the modifier has formula (XIX).
 21. The modified polyfarnesene of claim 20, wherein the modifier is allyl alcohol, hydroxymethyl vinyl ether, hydroxyehtyl vinyl ether, hydroxypropyl vinyl ether, hydroxybutyl vinyl ether, hydroxypentyl vinyl ether, hydroxyhexyl vinyl ether, hydroxyheptyl vinyl ether, hydroxycyclohexyl vinyl ether, allylglycidyl ether, p-glycidyloxy styrene, p-glycidyloxy-α-methyl styrene, p-(3,4-epoxycyclohexylmethyloxy) styrene, p-(3,4-epoxycyclohexylmethyloxy)-α-methyl styrene, glycidyl ethylene, 3,4-epoxycyclohexylmethylethylene, glycidylvinyl ether, 3,4-epoxycyclohexylmethyl vinyl ether, 3,4-epoxycyclohexylmethyl allyl ether or a combination thereof.
 22. The modified polyfarnesene of claim 13, wherein the modifier has formula (XX).
 23. The modified polyfarnesene of claim 22, wherein the modifier is bicyclo[2,2,2]-oct-5-ene-2,3-dicarboxylic acid anhydride, bicyclo[2,2,1]hept-5-ene-2,3-dicarboxylic acid anhydride or a combination thereof.
 24. The modified polyfarnesene of claim 13, wherein the reaction is carried out in the presence of the grafting initiator at a temperature from about 50 ° C. to about 300 ° C.
 25. The modified polyfarnesene of claim 24, wherein the grafting initiator is a dialkyl peroxide, a diacyl peroxide, a peroxyester, a peroxyketone, azobisisobutyronitrile or a combination thereof.
 26. The modified polyfarnesene of claim 13, wherein the polyfarnesene has formula (A):

wherein m is from 0 to about 100,000; n is from 1 to about 100,000 with the proviso that when m is 0, n is from 2 to about 100,000; X has one or more of formulae (I)-(VIII):

Y has formula (IX):

wherein R¹ has formula (XI):

R² has formula (XII):

R³ has formula (XIII):

and R⁴ has formula (XIV):

wherein each of R⁵, R⁶, R⁷ and R⁸ is independently H, alkyl, cycloalkyl, aryl, cycloalkenyl, alkynyl, heterocyclyl, alkoxy, aryloxy, carboxy, alkoxycarbonyl, aminocarbonyl, alkylaminocarbonyl, dialkylaminocarbonyl, acyloxy, nitrile or halo.
 27. The modified polyfarnesene of claim 26, wherein the amount of formula (I) is at most about 80 wt. % and the amount of formula (II) is from about 5 wt. % to about 99 wt. %, based on the total weight of the polyfarnesene.
 28. The modified polyfarnesene of claim 26, wherein the mole percent ratio of X to Y is from about 1:4 to about 100:1 when m is 1 or greater.
 29. The modified polyfarnesene of claim 26, wherein m is 0 and n is from 2 to about 100,000.
 30. The modified polyfarnesene of claim 26, wherein m is from 1 to about 100,000 and n is from 1 to about 100,000, and wherein the polyfarnesene is a random farnesene interpolymer.
 31. The modified polyfarnesene of claim 26, wherein m is from 1 to about 100,000 and n is from 1 to about 100,000, and wherein the polyfarnesene is a block farnesene interpolymer.
 32. A graft copolymer prepared by reacting the modified polyfarnesene of claim 13 with a condensation polymer at a temperature from about 50 ° C. to about 300 ° C., wherein the condensation polymer is a polyester, a polycarbonate, a polyamide, a polyether, a phenol-formaldehyde resin, an urea-formaldehyde resin, a melamine-formaldehyde resin or a combination thereof.
 33. The graft copolymer of claim 32, wherein the condensation polymer is a polyester, a polycarbonate, a polyamide or a combination thereof.
 34. The graft copolymer of claim 32, wherein the condensation polymer is a polyester.
 35. The graft copolymer of claim 34, wherein the polyester is a hydroxyl-terminated polyester.
 36. The graft copolymer of claim 34, wherein the polyester is a carboxyl-terminated polyester.
 37. The graft copolymer of claim 34, wherein the polyester is an epoxy-terminated polyester.
 38. The graft copolymer of claim 34, wherein the polyester is a polyethylene terephthalate.
 39. The graft copolymer of claim 38, wherein the polyethylene terephthalate is a hydroxyl-terminated polyethylene terephthalate.
 40. The graft copolymer of claim 38, wherein the polyethylene terephthalate is a carboxyl-terminated polyethylene terephthalate.
 41. The graft copolymer of claim 38, wherein the polyethylene terephthalate is an epoxy-terminated polyethylene terephthalate.
 42. The graft copolymer of claim 32, wherein the condensation polymer is a polycarbonate.
 43. The graft copolymer of claim 42, wherein the polycarbonate is a hydroxyl-terminated polycarbonate.
 44. The graft copolymer of claim 42, wherein the polycarbonate is an epoxy-terminated polycarbonate.
 45. The graft copolymer of claim 32, wherein the condensation polymer is a polyamide.
 46. The graft copolymer of claim 34, wherein the polyamide is an amino-terminated polyamide.
 47. The graft copolymer of claim 34, wherein the polyamide is a carboxyl-terminated polyamide.
 48. The graft copolymer of claim 34, wherein the polyamide is an epoxy-terminated polyamide.
 49. A polymer composition comprising the graft copolymer of claim 1; and at least an additive.
 50. The polymer composition of claim 49, wherein the additive is a filler, tackifier, slip agent, anti-blocking agent, plasticizer, antioxidant, blowing agent, blowing agent activator, UV stabilizer, acid scavenger, colorant or pigment, coagent, lubricant, antifogging agent, flow aid, processing aid, extrusion aid, coupling agent, cross-linking agent, stability control agent, nucleating agent, surfactant, flame retardant, antistatic agent or a combination thereof.
 51. The polymer composition of claim 49, wherein the additive is a filler.
 52. The polymer composition of claim 49, wherein the additive is a colorant.
 53. The polymer composition of claim 49, further comprising a second polymer.
 54. The polymer composition of claim 53, wherein the ratio of the graft copolymer to the second polymer is from about 1:99 to about 99:1.
 55. The polymer composition of claim 54, wherein the second polymer is a polyolefin, polyurethane, polyester, polyamide, styrenic polymer, phenolic resin, polyacrylate, polymethacrylate or a combination thereof.
 56. An article comprising the graft copolymer of claim
 1. 57. The article of claim 56, wherein the article is a molded article, film, sheet or foam.
 58. The article of claim 57, wherein the article is a molded article selected from toys, grips, soft touch handles, bumper rub strips, floorings, auto floor mats, wheels, casters, furniture and appliance feet, tags, seals, gaskets, automotive doors, bumper fascia, grill components, rocker panels, hoses, linings, office supplies, seals, liners, diaphragms, tubes, lids, stoppers, plunger tips, delivery systems, kitchen wares, shoes, shoe bladders, and shoe soles.
 59. An article comprising the polymer composition of claim
 49. 60. The article of claim 59, wherein the article is a molded article, film, sheet or foam.
 61. The article of claim 60, wherein the article is a molded article selected from toys, grips, soft touch handles, bumper rub strips, floorings, auto floor mats, wheels, casters, furniture and appliance feet, tags, seals, gaskets, automotive doors, bumper fascia, grill components, rocker panels, hoses, linings, office supplies, seals, liners, diaphragms, tubes, lids, stoppers, plunger tips, delivery systems, kitchen wares, shoes, shoe bladders, and shoe soles. 